*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?

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.

When both pipes are used, they fill the tank in 5 hours.

The difference of the reciprocals of the two positive integers is 1/18. How long would it take the teacher to grade the papers working alone? A larger pipe fills a water tank twice as fast as a smaller pipe.

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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.

For example, the reciprocal of 5 is 1/5 and 5 ⋅ 1/5 = 1. The sum of the reciprocals of the two positive integers is 3/10. Working together, they take inventory in 1.5 hours.

In this section, the applications will often involve the key word “reciprocal.” When this is the case, we will see that the algebraic setup results in a rational equation. How long would it take Audrey to record the inventory working alone? Jerry can lay a tile floor in 3 hours less time than Jake. How long would it take Jerry to lay the floor by himself? Jeremy can build a model airplane in 5 hours less time than his brother.

## Comments Solving Rational Equations Word Problems

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