Nice problem. Took me a while to solve too but word problems are my weak area so I need the practice. Anyway I figured I would propose an alternative solution for those (like me
) who aren't as good with the algebra.
You can also pick numbers to solve. (This is my 1st post so please bear with me. )
1) To piggy back off of @Zarrolou we have:
x = (660/A) - (660/B) and B = A(1+y/100)
2) From here you can pick numbers for A and B, noting that A should be smaller than B (since A takes more time to complete the job). Let's say A = 10 and B = 66.
3) Solving for x and y you get:
x= (660/10)-(660/66) = 66-10 = 56
66=10(1+y/100)......skipping some steps if you solve for y you get y=560.
Our target value is A's time: 660/A = 660/10 = 66
4) Now plug x and y into the answer choices and see which one gives you the target value (66):
A) x + 100x/y = 56 + 100(56)/560 = 56 + 10 = 66 **Bingo!!!**
I wont bother to write out the rest but if you plug in x and y into the remaining choices you get different values so (A) is the right answer choice. To me this method is much easier to comprehend. I tried the algebra many times and still couldn't figure it out. To each his own. Regardless there is no way I could do this in 2 minutes!!
Hope this helps.