Question

An experienced roofer with Stark Vegas roofing company can install a new roof in 24

hours. Together with a new trainee they can install a new roof in 15 hours. How long
would it take the trainee working by himself to install a new roof? Round to the nearest
tenth.

Answer 1

40 hours

Explanation:

This is an example of a work-rate-time problem

Since the experienced roofer can finish the job in 24 hours, his rate of work would be 1/24 (of the roof) per hour

Let the time taken by the trainee alone be x hours

His rate of work =
`(1)/(x)`

Together they finish the roof in 15 hours
So combined work rate =
`(1)/(15)`

Since combined rate = sum of individual rates we get

`(1)/(24) +(1)/(x) = (1)/(15)`

Move 1/24 to the right side:

`(1)/(x) = (1)/(15) - (1)/(24)`

`(1)/(x) =(24 - 15)/(24\cdot 15) = (9)/(360)\\\\`

Taking reciprocals on both sides

`x = (360)/(9) = 40 \;hours`