Question

Tanya can wash a car and vacuum its interior in 22 hours. Pat needs 55hours to do this same job. If Tanya and Pat work together, how many hours will it take them to clean a car?

Answer 1

1 hour 26 Minutes

Explanation:

Tanya needs 2 hours to do the job.

Pat needs 5 hours to do this same job.

Tanya's rate
`=(1)/(2)`

Pat's rate
`=(1)/(5)`

Let the number of hours it will take both of them =x

Rate when two of them work together
`=(1)/(x)`

Therefore:

`(1)/(2)+(1)/(5)=(1)/(x)\\$Taking lowest common multiple$\\(5+2)/(10)=(1)/(x)\\\\(7)/(10)=(1)/(x)\\\\$Cross multiply$\\7x=10\\x=1.43$ hours`

`0.43 X 60 =25.8 \approx 26$ minutes`

Therefore: 1.43 hour = 1 hour 26 Minutes

It will take both of them approximately 1 hour 26 minutes to the job.