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

The rate of the first machine is 1/4 job per hour;

The rate of the second machine is 1/3 job per hour;

Thus, the combined rate of the machines is 1/4+1/3=7/12 job per hour, which means that it takes 1/(7/12)=12/7 hours both machines to do the job.

Answer: C.

Suppose we change the wording of the problem to "It would take 2 machines 4 hours together to complete a large production" How would you solve for that ? I'm trying to better understand the nature of the problem. Thanks. My logic says the rate is still the same since it still is 4 hours. If so than what does it change?