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Algebra 2: Lesson 8-4 Rational Equation Word Problems
Learning Goals:
1) How do we setup and solve word problems involving rational equations?
Today we are going to talk about applications to the real world. We will focus on three different types of word
problems.
 Problems involving people or machines doing work
 Problems that involve percentages
 Problems that involve moving objects
Problems Involving People or Machines Doing Work

When problems involve two people working together on a job then their rates add and they can perform
the job working together in a shorter amount of time.

If we let x = time it takes 1 person to complete the task, then his work rate is . In other words, he can
complete the 1 job in x number of hours.
Example: Bill’s garden hose can fill the pool in 10 hours. His neighbor has a hose than can fill the pool in 15
hours. How long will it take to fill the pool using both hoses?
Equation needed in order to solve this problem:
Practice: Joe can complete his yard work in 3 hours. If his son helps it will take only 2 hours working together.
How long would the yard work take if his son is working alone?
Challenge: Norm and Cliff can paint the office in 5 hours working together. Being a professional painter, Norm
can paint twice as fast as Cliff. How long would it take Cliff to paint the office by himself?
Problems Involving Percentages

When problems involve percentages, think about setting up a proportion.
Example: So far in your volleyball practice, you have put into play 37 of the 44 serves you have attempted. Find
the number of consecutive serves you need to put into play in order to raise your serve percentage to 90%.
Equation needed in order to solve this problem:
Practice: Anne and Maria play tennis almost every weekend. So far, Anne has won
out of
How many matches will Anne have to win in a row to improve her winning percentage to
matches.
?
Challenge: You have a solution containing
acid and a solution containing
acid.
How much of the
solution must you add to liter of the
solution to create a mixture that is
acid?
Problems Involving Moving Objects

When objects are in motion, a variation of the distance formula must be used.

This formula can be manipulated in order to change it to a formula that will give a rational expression for
the time. This variation is Distance divided by Rate equals Time.
Example: Adam drives 15 mph faster than David does. Adam can drive 100 miles in the same amount of time
that David drives 80 miles. Find Adams driving speed.
Table used to help setup equation:
Distance
Adam
100
David
80
Rate
Time
Equation needed in order to solve this problem:
Practice: A passenger train can travel 20mph faster than a freight train. If the passenger train can cover 390
miles in the same time it takes the freight train to cover 270 miles, how fast is each train?
PRACTICE
DIRECTIONS: For the following problems, setup an appropriate equation that can be used to solve the question.
1. The first leg of Mary’s road trip consisted of 120 miles of traffic. When the traffic cleared she was able to
drive twice as fast for 300 miles. If the total trip took 9 hours how long was she stuck in traffic?
2. You have
liters of a juice blend that is
juice.
How many liters of pure juice need to be added in order to make a blend that is
juice?
3. Working together, Jennifer and Lori can plant a vegetable garden in 3 hours. If Lori works alone, it takes her 8
hours longer than it takes Jennifer to plant the garden. How long does it take Lori to plant the vegetable
Garden by herself?