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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