Bunuel wrote:

Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?

A. m/(m + n)

B. n/(m + n)

C. mn/(m + n)

D. mn/(m – n)

E. mn/(n – m)

Kudos for a correct solution.

This question seems tricky, but I hope that I have been able to crack it! Here's my solution:

Since we are asked to find the number of hours it takes Machine Q to manufacture 1500 jars, we need to first find the rate at which Machine Q operates. So Machine P has a rate of \(\frac{

1500}{m}\) because it can manufacture 1500 jars in m hours. Together, Machine P and Machine Q's combined rate (when working simultaneously) is \(\frac{

1500}{n}\), this is because it takes Machine P and Q n hours to manufacture 1500 jars when working together. Therefore Machine Q's rate is \(\frac{

1500}{n}\) \(

-\) \(\frac{

1500}{m}\), which simplifies to \(\frac{

1500*(m - n)}{mn}\). We need to find the number of hours it takes Machine Q to produce 1500 jars, so that would equal \(\frac{

1500}{(1500*(m - n))/mn}\), which simplifies to \(\frac{

mn}{(m - n)}\).

I think the answer is D!

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