Question

Ted can mow the lawn in 5 minutes by using his power mower. Galen takes 15 minutes to mow the same lawn using a push-type mower.

How many minutes would the job take if the two boys worked together?

Answer 1

3.75 minutes.

Explanation:

Let t represent the time taken by both to complete the work.

We have been given that Ted can mow the lawn in 5 minutes by using his power mower. So part of lawn mowed by Ted in one minute would be
`(t)/(5)`.

We are also told that Galen takes 15 minutes to mow the same lawn using a push-type mower. So part of lawn mowed by Galen in one minute would be
`(t)/(15)`.

Since both are mowing one lawn, so we can set an equation as:

`(t)/(5)+(t)/(15)=1`

`(3t)/(15)+(t)/(15)=1`

`(3t+t)/(15)=1`

`(4t)/(15)=1`

Cross multiply:

`4t=15`

`(4t)/(4)=(15)/(4)`

`t=3(3)/(4)`

`t=3.75`

Therefore, it will take 3.75 minutes for both to complete the job.