Question

Jimmy can oil the lanes in a bowling alley in eight hours. Perry can oil the same lanes in nine hours. How long would it take them if they worked together?

Answer 1

It would take
`4(4)/(17)` or 4.24 hours to oil the lanes if they work together.

Explanation:

Given:

Time to oil the lanes by Jimmy alone = 8 hours

Time to oil the lanes by Perry alone = 9 hours

Now, let the time taken by both working together be 'x' hours.

Part of the work done in 1 hour by Jimmy alone =
`(1)/(8)`

Part of the work done in 1 hour by Perry alone =
`(1)/(9)`

Part of the work done in 1 hour by Jimmy+Perry together =
`(1)/(x)`

Now, total work in 1 hour is given as:

`(1)/(8)+(1)/(9)=(1)/(x)\\\\(1* 9)/(8* 9)+(1* 8)/(8* 9)=(1)/(x)\\\\(9+8)/(72)=(1)/(x)\\\\(17)/(72)=(1)/(x)\\\\\textrm{Doing cross product, we get:}\\\\17x=72\\\\x=(72)/(17)=4(4)/(17)\ hours`

Therefore, it would take
`4(4)/(17)` or 4.24 hours to oil the lanes if they work together.