# High School Math : Setting up Equations

## Example Questions

### Example Question #1 : Equations

Tom is painting a fence  feet long. He starts at the West end of the fence and paints at a rate of  feet per hour. After  hours, Huck joins Tom and begins painting from the East end of the fence at a rate of  feet per hour. After  hours of the two boys painting at the same time, Tom leaves Huck to finish the job by himself.

If Huck completes painting the entire fence after Tom leaves, how many more hours will Huck work than Tom?

Explanation:

Tom paints for a total of  hours (2 on his own, 2 with Huck's help). Since he paints at a rate of  feet per hour, use the formula

(or )

to determine the total length of the fence Tom paints.

feet

Subtracting this from the total length of the fence  feet gives the length of the fence Tom will NOT paint:  feet. If Huck finishes the job, he will paint that  feet of the fence. Using , we can determine how long this will take Huck to do:

hours.

If Huck works  hours and Tom works  hours, he works  more hours than Tom.