XYZ Question

[deborahmirabal]

Question from MGMAT CAT Exam: Machine A, working alone at a constant rate, can complete a certain production lot in x hours. Machine B, working alone at a constant rate, can complete 1/5 of the same production lot in y hours. Machines A and B, working together, can complete 1/2 of the same production lot in z hours. What is the value of y in terms of x and z?


I was able to get the correct answer after adding the rates, however, why would I need to add the rates and not the times to find the answer? If adding the times, I get a different answer:

5y = 2z-x

y = (2z-x)/5

Please explain.

[tim]

that's the rule; when two machines are working together you add their rates. think of it this way: if i can answer 3 GMAT problems an hour and you can answer 4 problems an hour, together we can answer 7 per hour. on the other hand, if you turn this into times, it takes me 20 minutes to answer a problem and it takes you 15 minutes, but that certainly doesn't mean it takes us 35 minutes working together!