Question

Jim and Shirley, working together, can rake the yard in 3 hours. Working alone, Shirley takes three times as long as Jim. How long does it take Jim to rake the yard alone?

Answer 1

4 hours

Explanation:

Let time taken by Jim to rake be x hours

Jim's rate will be 1/x

Let y be time taken by Shirley to rake alone

Shirley's rate is 1/y which is equivalent to 1/3x since Shirley takes three times as long as Jim to imply Shirley's rate is slow

Total rate=1/x+1/3x=4/3x

Combined rate=4/3x which it takes them 3 hours hence a rate of 1/3

Therefore

4/3x=1/3

x=4 hours