You find the height, h, is equal to [latex] \frac{V}{\pi {{r}^{2}}}[/latex]. A student has received homework scores of 4, 8, 7, 7, and 9 and the first two exam scores are 78 and 83. I know you use the formula Distance=Rate*time ,d=r*t and to get the speed its d/t=r 2. :) https://www.patreon.com/patrickjmt !! Therefore, [latex] h=\frac{V}{\pi {{r}^{2}}}[/latex]. It takes Sam 4 hours to rake the front lawn while his brother, Dave, can rake the lawn in 2 hours. Only the general form of the equation has changed. Check the solution in the original equation. How long will it take the printer to get the magazine printed with both presses running together? Is 12 mph a reasonable speed for biking downhill? A beam with diagonal 6 inch will support a maximum load of 108 pounds. We also see problems dealing with plain fractions Problem 3 : A person travels at a speed of 60 miles per hour. Or 8 hours per 1 deck, which is the same thing as saying 1 deck per 8 hours. Find the actual distance from Chicago to Memphis. Solve an application using a formula that must be solved for a specified variable. [latex] \frac{V}{\pi {{r}^{2}}}=h[/latex]. This means the concentration is [latex]17[/latex] pounds of sugar to [latex]220[/latex] gallons of water. Simplify and rewrite the equation, solving for m. [latex]\begin{array}{l}v\cdot D=m\cdot \frac{v}{v}\\v\cdot D=m\cdot 1\\v\cdot D=m\end{array}[/latex]. 1. Find the speed of the Jim’s boat. A 2-foot-tall dog casts a 3-foot shadow at the same time a cat casts a one foot shadow. We are looking for the numbers of hours it will take them to paint the room together. Rational equations can be used to solve a variety of problems that involve rates, times, and work. 4 hours and 27 minutes to paint the room. ⓐ Write the equation that relates pressure to volume. If a job on Press #1 takes 6 hours, then in 1 hour of the job is completed. The following video gives another example of how to use rational functions to model mixing. What you do not know is how much time it will take to do the required work at the designated rate. This is a typical ‘work’ application. If we let s be her salary and h be the number of hours she has worked, we could model this situation with the equation. Rational equations can be used to solve a variety of problems that involve rates, times, and work. In the following exercises, the triangles are similar. We will discuss direct variation and inverse variation in this section. The equation can be used to find t, the number of hours it would take both of them, working together, to clean their apartment. In the next example, we will know the total time resulting from travelling different distances at different speeds. Rate Time Distance With the current x+1 5 Against the current x-1 6 Now fill in the chart like we did on the last example, that is, time equals distance over rate. Distance - Rate - Time Word Problems Date_____ Period____ 1) An aircraft carrier made a trip to Guam and back. We are looking for Jazmine’s running speed. If he works at a steady pace, in 1 hour he would paint of the room. Jazmine trained for 3 hours on Saturday. Substitute the given values for the variables. If person [latex]A[/latex] works at a rate of [latex]1[/latex] job every [latex]a[/latex] hours, and person [latex]B[/latex] works at a rate of [latex]1[/latex] job every [latex]b[/latex] hours, and if [latex]t[/latex] represents the total amount of time it takes to paint [latex]1[/latex] house, we have, [latex]\begin{align}W&= \left(r_1 + r_2\right)t \\ 1 &= \left(\dfrac{1}{a}+\dfrac{1}{b}\right)t \\ 1 &= \dfrac{t}{a}+\dfrac{t}{b}\end{align}[/latex]. A six foot tall person standing next to the tower casts a seven-foot shadow. Find the average speed of the trip there. https://www.youtube.com/watch?v=kbRSYb8UYqU&feature=youtu.be, http://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface, https://www.youtube.com/watch?v=ecEUUbRLDQs&feature=youtu.be, Solve a rational formula for a specified variable. The actual distance from New York to Chicago is 800 miles. Find the length of the indicated side. Washing his dad’s car alone, eight year old Levi takes 2.5 hours. In this case, you can add their individual work rates together to get a total work rate. Find the speed Darrin skateboards with no wind. Example 1 In a certain Algebra class there is a total of 350 possible points. His uphill speed was 8 miles per hour slower than his downhill speed. We will use similar triangles to write an equation. One cyclist rides twice as fast as the other. Find the rate of each cyclist. We will revisit that idea in the next example. Mixtures are made of ratios of different substances that may include chemicals, foods, water, or gases. Anya and Bill stained a large porch deck in 8 hours. How many calories are in 12 ounces of the drink? If she drives the rental car for 2 hours more than she rode the plane, find the speed of the car. The formula assumes we know r and t and use them to find D. If we know D and r and need to find t, we would solve the equation for t and get the formula. ⓐ Write the equation that relates c and t. ⓑ How many calories would he burn if he exercises for 90 minutes? Why or why not? If it took him 2 hours longer to ride uphill than downhill, what was his uphill rate? ⓐ Write the equation that relates the number of hours to the pump rate. Find her rate of jogging on the flat trail. Nathan walked on an asphalt pathway for 12 miles. This is their planting rate. The distances are given, enter them into the chart. Yes. For any proportion, we get the same result when we clear the fractions by multiplying by the LCD as when we cross-multiply. Ex 1: Rational Equation Application - Painting Together. ⓐ Write the equation that relates the car’s value to its age. The number of calories, c, burned varies directly with the amount of time, t, spent exercising. An introduction to solving word problems on uniform motion (rate-time-distance) using the formula rate x time = distance, or rt=d. • Fill in the Distance Column (d) with each distance given in the problem. After she reached the peak she rode for 12 miles along the summit. Brian can lay a slab of concrete in 6 hours, while Greg can do it in 4 hours. How long would it take Kristina to paint the room by herself? When the two gardeners work together it takes 2 hours and 24 minutes. ⓐ Write the equation that relates the cost, c, with the number of miles. It took her 2 hours less to ride back to college on the bus than it took her to ride home on her bike, and the average speed of the bus was 10 miles per hour faster than Kayla’s biking speed. Let t be the number of minutes since the tap opened. Start with the formula for the volume of a cylinder. So in 1 hour working together they have completed of the job. The basic equation was where D is the distance traveled, r is the rate, and t is the time. distance = rate x time When identifying the parts of the word problem, distance is typically given in units of miles, meters, kilometers, or inches. What is the speed of the boat? Working together, they can complete the job in [latex]24[/latex] hours. Find the height of the tree. One 12-ounce can of soda has 150 calories. Use a General Strategy to Solve Linear Equations, Solve Mixture and Uniform Motion Applications, Graph Linear Inequalities in Two Variables, Solve Systems of Linear Equations with Two Variables, Solve Applications with Systems of Equations, Solve Mixture Applications with Systems of Equations, Solve Systems of Equations with Three Variables, Solve Systems of Equations Using Matrices, Solve Systems of Equations Using Determinants, Properties of Exponents and Scientific Notation, Greatest Common Factor and Factor by Grouping, General Strategy for Factoring Polynomials, Solve Applications with Rational Equations, Add, Subtract, and Multiply Radical Expressions, Solve Quadratic Equations Using the Square Root Property, Solve Quadratic Equations by Completing the Square, Solve Quadratic Equations Using the Quadratic Formula, Solve Quadratic Equations in Quadratic Form, Solve Applications of Quadratic Equations, Graph Quadratic Functions Using Properties, Graph Quadratic Functions Using Transformations, Solve Exponential and Logarithmic Equations. So this 1 deck of per 8 hours, this is going to be equal to Anya's rate, 1/A decks per hour, plus Bill's rate. And this is going to be the combination of each of their rates. Cypress College Math Department – CCMR Notes Applications of Rational Equations, Page 1 of 7 Applications of Rational Equations Objective 1: Work Rate Problems If it takes me 5 hours to paint a room, then I can do 1/5 of the job in one hour. How long does it take his sister when she cleans the house alone? Hudson travels 1080 miles in a jet and then 240 miles by car to get to a business meeting. A telephone pole casts a shadow that is 50 feet long. How long does it take Levi’s dad to wash the car by himself? Laney wanted to lose some weight so she planned a day of exercising. Suppose we know that the cost of making a product is dependent on the number of items, xx, produced. This is summed up in the Property of Similar Triangles. Gary can do it in 4 hours. Mia can clean her apartment in 6 hours while her roommate can clean the apartment in 5 hours. If it takes Joe 2 hours longer than Ken to get to the game, what is Joe’s speed? Rate * time = distance. Her speed on the interstate was 15 more than on country roads. ⓑ How many cavities would Paul expect Lori to have if she had brushed her teeth for 2 minutes each night? On the map, Atlanta, Miami, and New Orleans form a triangle. [latex]C\left(12\right)=\frac{5+12}{100+10(12)}=\frac{17}{220}[/latex]. ⓐ Write the equation that relates the length of the spring to the weight. Rational Equations: Applications - Work Word Problems Here are a few examples Page 5/28. Ann, who works with her, can clean the salon in 30 minutes. This is sometimes called solving a literal equation. Using rational expressions and equations can help you answer questions about how to combine workers or machines to complete a job on schedule. A chart will help us organize the information. Kayla rode her bike 75 miles home from college one weekend and then rode the bus back to college. Simplify. His uphill speed was 5 mph slower than his downhill speed. The speed of the express train is 42 miles per hour faster than the speed of the bus. Phil wants to fertilize his lawn. ⓐ Write the equation that relates the number of hours to the pump rate. Marisol solves the proportion by ‘cross multiplying,’ so her first step looks like Explain how this differs from the method of solution shown in (Figure). In the following exercises, solve the application problem provided. If he drove 15 mph faster on the interstate than on the country roads, what was his rate on the country roads? example: A train can travel at a constant rate from New York to Washington, a distance of 225 miles. Each bag of fertilizer covers about 4,000 square feet of lawn. To solve applications with similar figures we will follow the Problem-Solving Strategy for Geometry Applications we used earlier. Joy can file 100 … Here is says that the total How long will it take the two working together? We are looking for the speed of the airplane. The pediatrician will prescribe 180 mg of fever reducer to Isabella. A new energy drink advertises 106 calories for 8 ounces. Paula and Yuki are roommates. If Ra’shon takes 7 hours, then in 1 hour, If Ra’shon’s sister takes s hours, then in. A circular pizza with a radius of 6 inches has an area of 113.04 square inches. When driving the 9-hour trip home, Sharon drove 390 miles on the interstate and 150 miles on country roads. Ronald needs a morning breakfast drink that will give him at least 390 calories. John’s rate: [latex] \frac{1}{3x}[/latex]. Answer: 9 … take notes and complete the problems below . ⓑ What load will a beam with a 10-inch diagonal support? Unit 15: Rational Expressions, from Developmental Math: An Open Program. The formula for finding the density of an object is [latex] D=\frac{m}{v}[/latex], where D is the density, m is the mass of the object, and v is the volume of the object. An important step in solving rational equations is to reject any extraneous … She jogs 1 mile per hour slower on the hilly trail than on the flat trail, and her return trip takes her two hours longer. The constant k is called the constant of variation. On a map, San Francisco, Las Vegas, and Los Angeles form a triangle. If Josiah drinks the big 32-ounce size from the local mini-mart, how many calories does he get? ⓑ How long would it take Ada to pump her basement if she used a pump rated at 400 gpm? Watch the following video for more examples of solving for a particular variable in a formula, a literal equation. How long would it take if the two gardeners worked together to mow the golf course? This is a distance problem, so we can use the formula where distance equals rate multiplied by time. An oatmeal cookie recipe calls for cup of butter to make 4 dozen cookies. Applications Word Problems Answers Solve applications with rational equations including revenue, distance, and work-rate problems : A rational expression is undefined where the denominator is zero. The express train can make the trip in two hours and the bus takes five hours for the trip. Work problems often ask us to calculate how long it will take different people working at different speeds to finish a task. The height of the Statue of Liberty is 305 feet. The fixed cost doesn’t change when more items are produced, whereas the variable cost increases as mor… The mass of a liquid varies directly with its volume. If we let t down denote the time of the downstream trip and t up the time of the upstream trip, we … ⓑ After looking at the checklist, do you think you are well-prepared for the next section? How many cups does he need to drink to reach his calorie goal? Yes. We are looking for how many hours it would take to complete the job with both presses running together. We can model this with the word equation and then translate to a rational equation. The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. The distance, he travels before stopping for lunch varies directly with the speed, he travels. What was Dennis’ speed going uphill and his speed going downhill? ⓑ What is the volume of this liquid if its mass is 128 kilograms? How long will it take them to rake the lawn working together? How long should the shadow of the statue be? If the first person does a job in time A, a second person does a job in time B, and together they can do a A negative speed does not make sense in this problem. We say that Lindsay’s salary varies directly with the number of hours she works. How tall is the pine tree? ⓐ Write the equation that relates d and t. ⓑ How many miles would it travel in 5 hours? In one hour Pete did of the job. Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. A diagram will help us visualize the situation. The uphill time is 2 more than the downhill time. Note, the cost function consists of a fixed cost ($15,000$15,000) and a variable cost (500x)(500x). Ra’shon can clean the house in 7 hours. Dana walked her dog for 7 miles but then had to run for 1 mile, spending a total time of 2.5 hours with her dog. Andrew’s morning … If two figures have exactly the same shape, but different sizes, they are said to be similar. Joon drove 4 hours to his home, driving 208 miles on the interstate and 40 miles on country roads. How long does it take for them to build a wall together? In the following exercises, answer each question. The algebraic models of such situations often involve rational equations derived from the work formula, W = rt.. The concentration after [latex]12[/latex] minutes is given by evaluating [latex]C\left(t\right)[/latex] at [latex]t=\text{ }12[/latex]. ⓑ What would it cost to travel 22 miles with this service? And together they did of the job. In applications using direct variation, generally we will know values of one pair of the variables and will be asked to find the equation that relates x and y. CHAPTER 11: RATIONAL EQUATIONS AND APPLICATIONS Chapter Objectives By the end of this chapter, students should be able to: Identify extraneous values Apply methods of solving rational equations to solve rational equations Solve applications with rational equations including revenue, distance, and work-rate … His uphill speed is 8 miles per hour slower. [latex]\begin{array}{l}1=\left( \frac{1}{x}+\frac{1}{3x} \right)24\\\\1=\left[ \frac{\text{1}}{\text{32}}+\frac{1}{3\text{(32})} \right]24\\\\1=\frac{24}{\text{32}}+\frac{24}{3\text{(32})}\\\\1=\frac{24}{\text{32}}+\frac{24}{96}\\\\1=\frac{3}{3}\cdot \frac{24}{\text{32}}+\frac{24}{96}\\\\1=\frac{72}{96}+\frac{24}{96}\end{array}[/latex]. We’ll, On the map, the distance from Los Angeles. We are looking for Hamilton’s downhill speed. Solved for rate [latex]r[/latex] the formula is [latex] r=\frac{W}{t}[/latex](divide both sides by t). Sam can paint a house in 5 hours. Including, number, distance and work problems. We solve inverse variation problems in the same way we solved direct variation problems. Rate Time Distance With the current x+1 5 Against the current x-1 6 To get the equation, we look back at the original problem. Orange juice has 130 calories in one cup. The work is painting [latex]1[/latex] house or [latex]1[/latex]. Find her walking speed. ⓐ Write the equation of variation. His jogging rate was 25 mph slower than the rate when he was riding. This is a uniform motion situation. What is his running speed? Using algebra, you can write the work formula [latex]3[/latex] ways: Solved for time [latex]t[/latex] the formula is [latex] t=\frac{W}{r}[/latex] (divide both sides by r). Two variables vary directly if one is the product of a constant and the other. [latex]C\left(0\right)=\frac{5+0}{100+10(0)}=\frac{5}{100}=\frac{1}{20}[/latex]. ⓐ Write the equation that relates the area to the radius. Ex 2: Solve a Literal Equation for a Variable. Thanks to all of you who support me on Patreon. Choose variables to represent the unknowns. Dennis’s uphill speed was 10 mph and his downhill speed was 5 mph. Find the speed of the bus. She went 50 miles before she got caught in a storm. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike? Word Problem Workbook Motion – Rational Equations 81 Time (t) = Distance (d) Rate (r) D r t Enter in your chart the information in the problem that refers to distance and its corresponding rate (speed). Ex: Rational Equation App - Find Individual Working Time Given Time Working Together. Darrin can skateboard 2 miles against a 4-mph wind in the same amount of time he skateboards 6 miles with a 4-mph wind. The equation that relates them is, For any two variables x and y, y varies inversely with x if, The word ‘inverse’ in inverse variation refers to the multiplicative inverse. At the same time, the shadow of a tree was 24 feet long. The equations for rate (r), distance (d), and time (t) are r d t t d ⇒ d=rt, r=, = Let x = speed in still water Let c = speed of the current The main difference with these problems is rate needs to be expressed using two variables because moving upstream the current is against you and downstream it moves with you. the number of minutes, m, on the treadmill. As one variable increases, the other decreases. His patient, Lori, had four cavities when brushing her teeth 30 seconds (0.5 minutes) each night. 7.3 Solving Linear Equations: ax + b = c 7.4 Solving Linear Equations: + b = cx + d 7.5 Working with Formulas 7.6 Applications: Number Problems and Consecutive Integers 7.7 Applications: Distance-Rate-Time, Interest, Average, and Cost 7.8 Solving Linear Inequalities 7.9 Compound Inequalities 7.10 Absolute Value Equations ⓐ Write the equation that relates c and m. ⓑ How many calories would he burn if he ran on the treadmill for 25 minutes? Keep in mind, it should take less time for two presses to complete a job working together than for either press to do it alone. Arnold burned 312 calories in 65 minutes exercising. ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. A boat travels 140 miles downstream in the same time as it travels 92 miles upstream. The following video shows an example of finding one person’s work rate given a known combined work rate. When two quantities are related by a proportion, we say they are proportional to each other. As shown above, many work problems can be represented by the equation [latex] \dfrac{t}{a}+\dfrac{t}{b}=1[/latex], where [latex]t[/latex] represents the quantity of time two people, [latex]A \text{ and } B[/latex], complete the job working together, [latex]a[/latex] is the amount of time it takes person [latex]A[/latex] to do the job, and [latex]b[/latex] is the amount of time it takes person [latex]B[/latex] to do the job. Rational formulas can be useful tools for representing real-life situations and for finding answers to real problems. Ken drives his car 30 mph faster Joe can ride his bike. Rational equations can be used to solve a variety of problems that involve rates, times and work. The length that a spring stretches varies directly with a weight placed at the end of the spring. The multiplicative inverse of x is. She ran 8 miles and then biked 24 miles. Example: Two cyclists start at the same corner and ride in opposite directions. Suppose Pete can paint a room in 10 hours. Rearrange the formula to solve for the mass (m) and then for the volume (v). Rational Expressions Applications Word Problems Rational Equations: Applications - Work Word Problems Here are a few examples of work problems that are solved with rational equations. The speed of the current is 6mph. $1 per month helps!! Work ... (such as distance over time). Jane spent 2 hours exploring a mountain with a dirt bike. 2. In the following exercises, write an inverse variation equation to solve the following problems. Joy can file 100 claims in 5 hours. Joe and John are planning to paint a house together. Some of the motion problems involving distance rate and time produce fractional equations. Alice can paint a room in 6 hours. Bill spent a total of 4 hours on the water. The formula to find the time when distance and speed are given is. Is 8 mph a reasonable running speed? Find the actual distance from Portland to Boise. ⓑ What is the frequency of a 10 inch string? Late one afternoon, his shadow was 8 feet long. Dennis went cross-country skiing for 6 hours on Saturday. At the current exchange rate, ?1 US is equal to ?1.3 Canadian. The problem states that it takes them [latex]24[/latex] hours together to paint a house, so if you multiply their combined hourly rate [latex] \left( \frac{1}{x}+\frac{1}{3x} \right)[/latex] by [latex]24[/latex], you will get [latex]1[/latex], which is the number of houses they can paint in [latex]24[/latex] hours. To solve applications with proportions, we will follow our usual strategy for solving applications But when we set up the proportion, we must make sure to have the units correct—the units in the numerators must match each other and the units in the denominators must also match each other. Try to do some now in your math textbook. The number of hours it takes for ice to melt varies inversely with the air temperature. The first observation to make, however, is that the distance, rate and time given to us aren't `compatible': the distance given is the distance for only \textit{part} of the trip, the rate given is the speed Carl can canoe in still water, not in a flowing river, and the time given is the duration of the \textit{entire} trip. It should take [latex]3[/latex] hours [latex]45[/latex] minutes for Myra and Francis to plant [latex]150[/latex] bulbs together. Danica can sail her boat 5 miles into a 7 mph headwind in the same amount of time she can sail 12 miles with a 7 mph tailwind. What was her speed on country roads? We divide the distance by the rate in each row, and place the expression in the time column. Applications of Rational … If Brian and Greg work together, how long will it take? Gary can do it in 4 hours. He burned 315 calories when he used the treadmill for 18 minutes. The cost of a ride service varies directly with the distance traveled. If his dad helps him, then it takes 1 hour. He walked the 12 miles back to his car on a gravel road through the forest. Joseph is traveling on a road trip. ⓑ How many vibrations per second will there be if the string’s length is reduced to 20 inches by putting a finger on a fret? The frequency of a guitar string varies inversely with its length. Myra: [latex] \frac{50\,\,\text{bulbs}}{2\,\,\text{hours}}[/latex] or [latex] \frac{25\,\,\text{bulbs}}{1\,\,\text{hour}}[/latex], Francis: [latex] \frac{45\,\,\text{bulbs}}{3\,\,\text{hours}}[/latex] or [latex] \frac{15\,\,\text{bulbs}}{1\,\,\text{hour}}[/latex]. Then she drove 68 miles at 9 mph less than she had driven when the weather was good. 2. If they work together, how long would it take them to clean the apartment? What is the speed of the car? The walk on the gravel took one hour longer than the walk on the asphalt. It averaged 6 km/h on the return trip. How many cups of butter will she need? For example, the two triangles in (Figure) are similar. The number of hours it takes Jack to drive from Boston to Bangor is inversely proportional to his average driving speed. If the dosage is 5 mg for every pound, how much medicine was Sunny given? The jet goes 300 mph faster than the rate of the car, and the car ride takes 1 hour longer than the jet. If you missed this problem, review (Figure). Maurice is traveling to Mexico and needs to exchange ?450 into Mexican pesos. Other work problems take a different perspective. If Isabella weighs 12 kg, how many milligrams of the fever reducer will the pediatrician prescribe? The distance between the cities is measured in inches. For any two variables x and y, y varies directly with x if. Let’s say you’d like to calculate how long it will take different people working at different speeds to finish a task. Ken and Joe leave their apartment to go to a football game 45 miles away. Lindsay’s salary is the product of a constant, 15, and the number of hours she works. Enter the hours per job for Pete, Alicia, and when they work together. This is given by the equation C(x)=15,000+500xC(x)=15,000+500x. Mixture problems become mathematically interesting when components of the mixture are added at different rates and concentrations. The actual distance from Seattle to Boise is 400 miles. When pediatricians prescribe acetaminophen to children, they prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of the child’s weight. You may recall the formula that relates distance, rate and time, [latex]d=rt[/latex]. Is that a greater concentration than at the beginning? This is a ‘work’ application. Rational Function Application - Concentration of a Mixture. She has asked the printer to run an extra printing press to get the printing done more quickly. 4.3 Rational Inequalities and Applications 345 5miles = rate traveling upstream time traveling upstream 5miles = (6 R)miles hour time traveling upstream The last piece of information given to us is that the total trip lasted 3 hours. Dana enjoys taking her dog for a walk, but sometimes her dog gets away, and she has to run after him. An airplane can fly 200 miles into a 30 mph headwind in the same amount of time it takes to fly 300 miles with a 30 mph tailwind. Notice in the last example that when we cleared the fractions by multiplying by the LCD, the result is the same as if we had cross-multiplied. How long will it take the two of them working together? Problems Answerssituations with work rate, variations, water current and speed of wind. How many bags of fertilizer will he have to buy? Josephine can correct her students test papers in 5 hours, but if her teacher’s assistant helps, it would take them 3 hours. Our first example of a uniform motion application will be for a situation similar to some we have already seen, but now we can use two variables and two equations. Rational Equations Word-Problems 5 6= The combined rate is the sum of the rates tank/hr. What is the speed of the airplane? a) 17 4𝑥𝑥−32. How long would it take them to clean the shop if they work together? ⓐ Write the equation that relates the string length to its frequency. For every 1 kilogram (kg) of a child’s weight, pediatricians prescribe 15 milligrams (mg) of a fever reducer. Jim’s speedboat can travel 20 miles upstream against a 3-mph current in the same amount of time it travels 22 miles downstream with a 3-mph current speed . completed/hour by Pete and then by Alicia. Kevin wants to keep his heart rate at 160 beats per minute while training. Byron wanted to try out different water craft. ⓐ Write the equation that relates the mass to the volume. John can fly his airplane 2800 miles with a wind speed of 50 mph in the same time he can travel 2400 miles against the wind. Enter the hours per job for Ra’shon, his, The part completed by Ra’shon plus the part, It would take Ra’shon’s sister 5 hours and. His biking speed is 6 mph faster than his running speed.