# A Guide to the GRE/Work and Time Problems

## Works & Time Problems

On a work and time problem, calculate how much work each person does in one hour and solve using these fractions.

Crew A can clean up the lot in 7 hours. Crew B can do it in 5 hours. How long will it take both crews to clean up the lot together?

Crew A can do 1/7 of the work per hour while Crew B can do 1/5 of the work per hour. Combined they can do 1/7+1/5 = 5/35+7/35 = 12/35 per hour. This means it will take them 35/12 hours, or 2.91666...67, to finish.

### Practice

1. Hal can paint a barn in 6 hours. Mary can do it in 9 hours. How long will it take them to paint the barn if they work together?

2. It takes Stephanie 4 hours to fix a tractor, while it takes Bruce 5 hours. How long will it take Stephanie and Bruce to fix the tractor if they work together?

3. Division I takes 11 hours to complete a report, while Division II takes 12 hours to complete one. How long will it take both divisions to complete a report if they work together?

1. hours

Hal's rate: barns painted per hour.

Mary's rate: barns painted per hour.

Their combined rate: += += barns painted per hour.

Their time to paint one barn:== =hours.

2. hours

Stephanie's rate: tractors fixed per hour.

Bruce's rate: tractors fixed per hour.

Their combined rate: += += tractors fixed per hour.

Their time to fix one tractor:== =hours.