Problem Solving

By themselves, crane operators A, B, and C can load a particular ship with containers in 5 hours, 7 hours, and 8 hours, respectively. What is the ratio of the time that it takes crane operators B and C to load this ship, working together at their individual rates, to the time it takes crane operator A working alone at her respective rate?


(A) 12/13

(B) 58/75

(C) 56/75

(D) 56/99

(E) 56/113

OA is C

I got the correct answer, but my ratio was inverted.

When you combine B and C you get 15/56. The ratio between those two and A is then (15/56)/(1/5), correct? When I multiplied the top by 5/1 I got 75/56. I knew that the top number needed to be smaller so I went with C, but I'd like to understand why my ratio was inverted. What did I do incorrectly?

Thanks.

They are looking for time and your answer is in rates. All you have to do is inreverse the rate to get time.

That makes sense. Thanks.