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How fast can Jerry paddle the kayak in still water? It takes a light aircraft 1 hour more time to fly 360 miles against a 30-mile-per-hour headwind than it does to fly the same distance with it. If the teacher helps, then the grading can be completed in 20 minutes. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. On the return trip, he was able to average 14 miles per hour faster than he averaged on the trip to town. The return trip downstream with the 1-mile-per-hour current took 1 hour less time. How long would it take Bryan to prepare and paint the house by himself? How long would it take his assistant to assemble a computer working alone? The teacher’s assistant can grade class homework assignments by herself in 1 hour.
If Jerry starts the job and his assistant joins him 1 hour later, then how long will it take to lay the floor? Working alone, Monique takes 6 hours to record the inventory of the entire shop, while it takes Audrey only 4 hours to do the same job.
How long will it take them working together if Monique leaves 2 hours early?
Example 1: A positive integer is 4 less than another. Example 2: A positive integer is 4 less than another. Working together, they need 6 hours to build the plane. Jeremy can paint the same shed by himself in 8 hours. Working with an assistant, he can assemble 10 computers in 6 hours.
The sum of the reciprocals of the two positive integers is 10/21. Solution: Begin by assigning variables to the unknowns. If the reciprocal of the smaller integer is subtracted from twice the reciprocal of the larger, then the result is 1/30. Solution: Answer: Two sets of positive integers solve this problem: and . The difference between the reciprocals of two consecutive positive odd integers is 2/15. How long would it take Jeremy to build the model airplane working alone? How long will it take them to paint two sheds working together? How long would it take his assistant to assemble 1 computer working alone? Jerry can lay a tile floor in 3 hours, and his assistant can do the same job in 4 hours.
The process I want you to take home from this lesson is one that can be applied to all rational equations. I remember this step easily by thinking of the first step I usually take when adding or working with regular fractions. Because rational equations can involve variables, finding our common denominator is slightly different than when working with regular fractions. What you do is you look at the various denominators that you have, and all you need to do is make sure that your common denominator has all the denominators in it and multiplied together.
It's not hard, and I will give you helpful tips on how to remember each step. A good way to remember this first part of solving the problem is to think about what identifies a rational equation. Our problem has denominators of 3 and 5, so our common denominator will be 3 * 5.
The difference of the reciprocals of two consecutive positive even integers is 1/24. If Bill can walk 3 miles in the same time it takes Mary to run 7.2 miles, then what is Bill’s average walking speed? An airplane traveling with a 20-mile-per-hour tailwind covers 270 miles. A jet airliner traveling with a 30-mile-per-hour tailwind covers 525 miles in the same amount of time it is able to travel 495 miles after the tailwind eases to 10 miles per hour. If the total trip took 5 hours, then at what speed can Jane row in still water? Jose drove 15 miles to pick up his sister and then returned home. Working with an associate, she completes the route in 4 hours.
The difference of the reciprocals of two consecutive positive odd integers is 2/99. If the passenger car can travel 231 miles in the same time it takes the aircraft to travel 455 miles, then what is the average speed of each? Mary can run 1 mile per hour more than twice as fast as Bill can walk. What is the average speed of the boat in still water? Jane rowed her canoe against a 1-mile-per-hour current upstream 12 miles and then returned the 12 miles back downstream. How long will it take them to detail a car working together? Jose can build a small shed by himself in 26 hours. How long would it take them to build the shed working together? Allison can complete a sales route by herself in 6 hours.
Try it risk-free Follow the steps you will learn in this video lesson to help you solve rational equation problems. A rational equation is just an equation that has fractions.
See how the process turns what looks like a huge problem into a much simpler and easier to manage problem. These fractions might just be numbers, but they also may be polynomials with numbers and letters in them.