### About Applications of Rational Expressions:

When learning how to solve applications of rational expressions, we generally encounter two scenarios. First, we will look at motion word problems. These problems involve the use of the distance formula. Second, we will look at work rate problems. These problems involve measuring individual rates of work in order to determine how fast a job can be completed.

Test Objectives

- Demonstrate the ability to set up a rational equation based on the information given in a word problem
- Demonstrate the ability to solve a rational equation and reject extraneous solutions
- Demonstrate the ability to check the solution to a word problem

#1:

Instructions: Solve each word problem.

a) It takes Heather nine hours to pick forty bushels of apples. Jack can pick the same amount in fourteen hours. How long would it take them if they worked together?

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#2:

Instructions: Solve each word problem.

a) Working alone, Kristin can clean an attic in nine hours. One day, her friend Julia helped and it only took six hours. How long would it take Julia to do it alone?

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#3:

Instructions: Solve each word problem.

a) A winery has a vat to hold white wine. An inlet pipe can fill the vat in six hours while an outlet pipe can empty it in twenty-one hours. How long would it take to fill the vat if both pipes are left open?

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#4:

Instructions: Solve each word problem.

a) Jane went to visit her brother Jacob at school. During the first part of her drive, she averaged seventy-four mph. For the second part, she hit heavy construction and was only able to average fifty mph. The distance for the second half of the trip was three hundred forty miles less than for the first. What was the total driving distance if she spent two hours more on the first part of the drive than the second?

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#5:

Instructions: Solve each word problem.

a) Carl can travel sixty miles downstream in the same time it takes to go eighteen miles upstream. If the speed of the boat is thirteen mph in still water, what is the speed of the current?

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Written Solutions:

#1:

Solutions:

a) It takes 126/23 hours for Jack and Heather to pick forty bushels of apples.

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#2:

Solutions:

a) It would take 18 hours for Julia to clean the attic alone.

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#3:

Solutions:

a) After 42/5 hours, the vat will be full.

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#4:

Solutions:

a) The total distance for the trip was 1140 miles.

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#5:

Solutions:

a) The speed of the current is 7 mph.