4.5 Rational Word Problems

Front

What is the formula to find the combined work rate of two people working together?

Back

The combined work rate is found by adding their individual work rates: 1/A + 1/B = 1/T, where A and B are the times taken by each person to complete the task alone, and T is the time taken when working together.

Front

If Peter can mow the lawn in 40 minutes and John in 60 minutes, how do you calculate their combined time?

Back

First, find their rates: Peter's rate = 1/40, John's rate = 1/60. Combined rate = 1/40 + 1/60 = 1/T. Solve for T to find T = 24 minutes.

Front

How long does it take for two people to complete a task together if one takes 5 hours and the other takes 4 hours?

Back

Use the formula: 1/5 + 1/x = 1/4, where x is the time taken by the second person alone. Solve for x to find that it takes 20 hours for the second person.

Front

What is the work rate of a person who can complete a task in 3 hours?

Back

The work rate is 1/3 of the task per hour.

Front

If Lucy can wash a car in 3 hours and together with Quinn they can wash it in 1 hour, how do you find Quinn's time?

Back

Set up the equation: 1/3 + 1/x = 1, where x is Quinn's time. Solve for x to find that it takes Quinn 1.5 hours.

Front

What is the individual work rate of Melanie if she can reupholster furniture in 5 hours?

Back

Melanie's work rate is 1/5 of the task per hour.

Front

If Keith and Melanie can complete a task together in 3 hours, how do you find Keith's time alone?

Back

Use the equation: 1/5 + 1/x = 1/3, where x is Keith's time. Solve for x to find that it takes Keith 7.5 hours.

Front

How do you calculate the time taken when two people work together on a task?

Back

Add their individual rates: 1/A + 1/B = 1/T, then solve for T.

Front

If Fran can clean the garage in 3 hours and Angie in 4 hours, how do you find their combined time?

Back

Calculate their rates: 1/3 + 1/4 = 1/T. Solve for T to find that it takes them 1.7 hours together.

Front

What is the significance of finding a common denominator when adding fractions in work problems?

Back

Finding a common denominator allows you to accurately add the individual work rates to find the combined work rate.