MathRevolution wrote:

[GMAT math practice question]

Machine A can produce balls at a constant rate of 2 balls per hour, and machine B can produce balls at a constant rate of 3 balls per hour. If at least one of machine A and machine B produces balls at any time, what is the smallest possible number of hours that machine A and machine B must work together at their constant rates to produce 70 balls in 20 hours?

A. 5hrs

B. 6hrs

C. 7hrs

D. 8hrs

E. 9hrs

Machine A's rate - 2 balls/hr

Machine B's rate - 3 balls/hr

Together, the machines produce 5 balls in an hour.

If the machines need to produce 70 balls in 20 hours, in order to use both the machines

for the smallest number of hours(let's call it x), we need to use Machine B for the rest of

the time

5x + 3(20 - x) = 70

5x + 60 - 3x = 70

2x = 10 -> x = 5

Therefore, the smallest possible number of hours both the machines work together is

5(Option A)
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