Question

Working​ together, it takes two roofers 12 hours to put a new roof on a portable classroom. if the first roofer can do the job by himself in 16 ​hours, how many hours will it take the second roofer to do the job by​ himself?

Answer 1

Let r and s be the respective rates in roofs per hour.

`12 = 1/(r+s)`

`r+s=1/12`

`s= -r + \frac 1 {12}`

`16=1/r`

`r=1/16`

`s= - \frac 1{16} + \frac 1 {12}[tex] = -(3)/(48) + (4)/(48) = (1)/(48)`

The second worker's rate is 1/48 roofs per hour or one roof every 48 hours.