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?	Choices.
A) m/(m + n)  B) n/(m + n)  C) mn/(m + n)  D) mn/(m – n)  E) mn/(n – m)
“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? ”   Since the number “1500 jars” appears over and over, let’s arbitrarily say 1500 jars = 1 lot, and we’ll use units of lots per hour to simplify our calculations.   P’s individual rate is (1 lot)/(m hours) = 1/m. The combined rate of P &amp; Q is (1 lot)/(n hours) = 1/n. We know   (P’s rate alone) + (Q’s rate alone) = (P and Q’s combined rate)   (Q’s rate alone) = (P and Q’s combined rate) – (P’s rate alone)   (Q’s rate alone) = 1/n – 1/m = m/ (nm) – n/ (nm) = (m – n)/(nm)   We now know Q’s rate, and we want the amount of 1 lot, so we use the “art” equation.   1 = [(m – n)/ (nm)]*T   T = (mn)/(m – n)   Answer = mn/(m – n)
<result>D</result>
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?