Walkabout wrote:

It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?

(A) 7/12

(B) 1 1/2

(C) 1 5/7

(D) 3 1/2

(E) 7

We can classify this problem as a “combined worker” problem. To solve this type of problem we should use the formula:

Work (done by worker 1) + Work (done by worker 2) = Total Work Completed

It takes machine one 4 hours to complete a job, so the rate of machine one is ¼. It takes machine two 3 hours to complete a job, so the rate of machine two is 1/3. Since we know they are both working together to complete the job, we can label this unknown time as “t” for each machine during the time that both machines are working together. Since rate x time = work, we can multiply to get the work completed for each machine.

Finally, we can plug our two work values into the combined work formula and determine t. Since the job is completed, the total work completed is 1.

Work (done by worker 1) + Work (done by worker 2) = Total Work Completed

(1/4)t + (1/3)t = 1

Multiplying the entire equation by 12 gives us:

3t + 4t = 12

7t = 12

t = 12/7 = 1 5/7

Answer is C.

_________________

Jeffrey Miller

Jeffrey Miller

Head of GMAT Instruction