### About Applications of Rational Equations:

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) A boat can go 36 miles against the current in the same amount of time that it takes to go 156 miles with the current. If the current is 5 miles per hour, how fast does the boat travel in still water?

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#2:

Instructions: solve each word problem.

a) Heather, a traveling salesperson first drove 1200 miles from Alberta to Prairieville. For her second trip, she drove 975 miles from Prairieville to Atlanta. If the two trips took the same amount of time and Heather’s speed on the second trip was 15 miles per hour slower than on the first trip, how fast was she driving on each trip?

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#3:

Instructions: solve each word problem.

a) Working alone, it takes Amanda 12 hours to cut the field. Her brother James can cut the same field in only 4 hours. How long would it take to cut the field if they work together?

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#4:

Instructions: solve each word problem.

a) Working together, Jason and Peter can pressure wash a parking lot in 4 hours. When Jason works alone, it takes him 20 hours. How long does it take Peter when he works alone?

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#5:

Instructions: solve each word problem.

a) A local welding shop uses water tanks for cooling purposes. The inlet pipes can fill an empty water tank in 5 hours, while the outlet pipe takes 10 hours to empty a full water tank. If both pipes are turned on at the same time, how long would it take to fill a completely empty water tank?

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Written Solutions:

#1:

Solutions:

a) 8 miles per hour

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#2:

Solutions:

a) First trip 80 miles per hour, second trip 65 miles per hour

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#3:

Solutions:

a) 3 hours

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#4:

Solutions:

a) 5 hours

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#5:

Solutions:

a) 10 hours