Word Problem

Question

Tom can rebuild an engine in 42 hours. His wife can rebuild the same engine in 36.5 hours. How long does it take them to rebuild an engine together?

Answer 1

(1/42)T = amount of the job Tom can do in T hours

(1/36.5)T = amount his wife can do in T hours

(1/42)T + (1/36.5)T = 1, i.e. working together they do the whole job in T hours.

Therefore

(1/42) + (1/36.5) = 1/T (as long as T is not 0)

This simplifies to

x = 42*73/(73 + 84)...and I will let you figure out how that fraction simplified and what the numeric answer is.