Once we have mastered rational expressions, we venture into applications of rational expressions. These word problems typically involve motion problems (distance = rate x time) and rate of work problems (how fast two or more people can complete a job given their individual rate of work).

Test Objectives
• Demonstrate the ability to find the LCD for a group of rational expressions
• Demonstrate the ability to solve an equation with rational expressions
• Demonstrate the ability to solve a word problem with rational expressions
Rational Equation Word Problem Practice Test:

#1:

Instructions: Solve each word problem.

a) Working alone, Adam can tar a roof in five hours. Jake can tar the same roof in eight hours. How long would it take to tar the same roof if they worked together?

#2:

Instructions: Solve each word problem.

a) Working alone, it takes Ryan 9 hours to stock and zone the canned soup aisle in a grocery store. Cesar can perform the same task in 11 hours. How long would it take if they work together?

#3:

Instructions: Solve each word problem.

a) A boat can go 102 miles downstream in the same amount of time that it can go 78 miles upstream. If the current speed is 4mph, how fast does the boat travel in still water?

#4:

Instructions: Solve each word problem.

a) A plane goes 1290 miles with the wind in the same amount of time as it goes 1210 miles against the wind. If the wind speed is 8mph, how fast does the plane travel in still air?

#5:

Instructions: Solve each word problem.

a) Working together, Mike and Steven can build a home in 5 weeks. Had he done it alone it would have taken Steven 12 weeks. How long would it take Mike to do it alone?

Written Solutions:

#1:

Solutions:

a) When Adam and Jake work together, they can tar the roof in 40/13 hours.

#2:

Solutions:

a) When Cesar and Ryan work together, they can stock and zone the aisle in 99/20 hours.

#3:

Solutions:

a) The boat would travel 30mph in still water.

#4:

Solutions:

a) The plane would travel 250mph in still air.

#5:

Solutions:

a) If Mike worked alone, he would take 60/7 weeks to build the house.