Machine A and Machine B are each used to make 660 widgets. It takes Machine A x hours longer to produce 660 widgets than Machine B. Machine B produces y% more widgets per hour than Machine A. How long does it take Machine A to make 660 widgets?

This one is tough. I keep getting tangled in the algebra. The answer choices have x and y, so I know I need to express A's time in terms of those variables, but the algebra is messy.

I think the key is to set B's time as t, so A's time is t + x. Then use the rate relationship: B's rate is y% more than A's rate. That gives 660/t = (1 + y/100) * (660/(t+x)). Then solve for t+x. But it's easy to make a mistake in the algebra.

This is a classic GMAT problem. I've seen similar ones where the answer is x + 100x/y. But I always forget the exact manipulation. Does anyone have a quick way to remember?

I think the trick is to realize that the time difference x corresponds to the extra time A takes. And the percentage difference y means B's rate is (100+y)% of A's rate. So if A's time is T, then B's time is T - x, and their rates are 660/T and 660/(T-x). Then 660/(T-x) = (1 + y/100) * 660/T. Solving gives T = x + 100x/y. So answer A.