Question

One roofer can put a new roof on a house three times faster than another. Working together they can roof a house in 5 days. How

many days would it take the faster roofer to put a new roof on a house working alone? Round the answer to the nearest tenth.

Answer 1

6.7 days

Explanation:

If t is the time the faster roofer takes, then the slower one takes 3t. Their combined rates in roofs per day are ...

1/t + 1/(3t) = 1/5

4/(3t) = 1/5 . . . . . . combine terms

t = 5(4/3) = 20/3 ≈ 6.7 . . . . multiply by 5t

The faster roofer working alone can roof a house in about 6.7 days.