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 long would it take the faster roofer working alone?

Answer 1

if A = 3 B A is 3 times faster than B

B + 3 B = 4 B speed of two working together

S = 4 B *5 = 20 B time to complete roof

It would take B 20 days to complete the roof

A = 20 / 3 = 6.67 days

Check:

B completes 1/20 roof / day

A completes 3/20 roof / day

Together they complete 4/20 or 1/5 roofs / day