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.

$12 = 1/(r+s)$

$r+s=1/12$

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

$16=1/r$

$r=1/16$

$s= - \frac 1{16} + \frac 1 {12}[tex] = -\frac{3}{48} + \frac{4}{48} = \frac{1}{48}$

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