Solving Rational Equations and Word Problems

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one fraction whose numerator and/or denominator is a polynomial.

Front

How do you find the combined work rate of two or more people working together?

Back

To find the combined work rate, add the individual work rates of each person. The work rate is calculated as 1 divided by the time taken to complete the task.

Front

If Sam can paint a room in 6 hours, what is his work rate?

Back

Sam's work rate is 1/6 of a room per hour.

Front

If Jenna can paint a room in 4 hours, what is her work rate?

Back

Jenna's work rate is 1/4 of a room per hour.

Front

If Francisco can paint a room in 12 hours, what is his work rate?

Back

Francisco's work rate is 1/12 of a room per hour.

Front

How do you calculate the time taken for two people to complete a task together?

Back

Use the formula: 1/(1/A + 1/B) where A and B are the times taken by each person to complete the task alone.

Front

If Bob can paint a fence in 5 hours, what is his work rate?

Back

Bob's work rate is 1/5 of a fence per hour.

Front

If Jen and Bob together can paint a fence in 2 hours, how do you find Jen's work rate?

Back

First, find the combined work rate (1/2), then subtract Bob's work rate (1/5) to find Jen's work rate.

Front

What is the formula to find the time taken for one person to complete a task if they work with another person?

Back

If A can do the job in x hours and they work together with B to complete it in y hours, then B's time can be found using the formula: 1/y = 1/x + 1/B.

Front

If Keith and Melanie can reupholster furniture in 3 hours together, what is their combined work rate?

Back

Their combined work rate is 1/3 of the job per hour.