CCA2 Module 1

Lesson 27: Word Problems Leading to Rational Equations

Exercise 1

Anne and Maria play tennis almost every weekend. So far, Anne has won 12 out of 20 matches.

  1. How many matches will Anne have to win in a row to improve her winning percentage to 75%?
  1. How many matches will Anne have to win in a row to improve her winning percentage to 90%?
  1. After Anne has reached a winning percentage of 90% by winning consecutive matches, how many matches can she now lose in a row to have a winning percentage of 50%?

Example 1

Fay takes 5 hours to paint a room. Rob can do the job in 10 hours. How long will it take them if they work together? (Consider this: How much of the whole job can Fay accomplish in one hour? Rob?)

Example 2

Pat, Frank, and Pam can wallpaper an apartment in 20 hours. Pam can do the job in 35 hours and Pat can do the job in twice the time it would take Frank. How long would it take Frank to do the job alone? Pat?

Exercise 2

Melissa walks 3 miles to the house of a friend and returns home on a bike. She averages 4 miles per hour faster when cycling than when walking, and the total time for both trips is two hours. Find her walking speed. (Recall: distance equal rate times time)

Exercise 3

You have 10 liters of a juice blend that is 60% juice.

  1. How many liters of pure juice need to be added in order to make a blend that is 75% juice?
  1. How many liters of pure juice need to be added in order to make a blend that is 90% juice?
  1. Suppose you added 15 liters of juice to the original 10 liters. What is the percentage of juice in this blend?

Exercise 4

  1. How much pure acid must be added to 50 mL of a 35% acid solution to produce a mixture that is 75% acid?
  1. You have a solution containing 10% acid and a solution containing 30% acid. How much of the 30% solution must you add to 1 liter of the 10% solution to create a mixture that is 22% acid?

Practice

  1. A glassblower can produce a set of simple glasses in about 2 hours. When the glassblower works with an apprentice, the job takes about 1.5 hours. How long would it take the apprentice to make a set of glasses when working alone?
  1. Robert can move a truckload of boxes in8 hours. Ed takes 12 hours to do the same job. How long would it take them to do the job working together?
  1. Susan can paint her house in 16 hours. Susan and Jeanne can paint it together in 10 hours. Find Jeanne’s rate of work. How long would it take Jeanne to do the job alone?
  1. Working together, Amy, Holly, and Keith can rake a lawn in 8 hours. Alone, it takes Amy twice the time it takes Keith, and Holly can do it in 16 hours by herself. Find the time it would take Amy and Keith to rake the lawn alone.