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Working alone, pump A can empty a pool in 3 hours...

This topic has 1 expert reply and 0 member replies

Working alone, pump A can empty a pool in 3 hours...

Post Fri Jan 12, 2018 2:15 pm
Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how how many minutes will it take pump A and pump B to empty the pool?

(A) 72
(B) 75
(C) 84
(D) 96
(E) 108

The OA is A.

I'm confused with this PS question. Experts, any suggestion? I don't know how can I solve it. Thanks in advance.

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Post Sat Jan 13, 2018 8:51 am
Hello LUANDATO.

Let's take a look at your question.

Working alone, pump A can empty a pool in 3 hours, it implies that pump A wor at a rate 1/3 pool/hour.
Working alone, pump B can empty a pool in 2 hours, it implies that pump A wor at a rate 1/2 pool/hour.

Working together the rate will be equal to $$\frac{1}{3}+\frac{1}{2}=\frac{5}{6}\ \text{pool per hour}$$. Now we have the following: $$\frac{5\ }{6\ }\ \frac{pool}{60\ \min}=1\ \frac{pool}{x}\ \Leftrightarrow\ x=72\ \min.$$ This is why the correct answer is the option A=72.

I hope this answer may help you.

I'm available if you'd like a follow-up.

Regards.

_________________
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