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.
Working alone, pump A can empty a pool in 3 hours...
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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 [spoiler]A=72[/spoiler].
I hope this answer may help you.
I'm available if you'd like a follow-up.
Regards.
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 [spoiler]A=72[/spoiler].
I hope this answer may help you.
I'm available if you'd like a follow-up.
Regards.
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The combined rate of pumps A and B is:BTGmoderatorLU wrote: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
1/3 + 1/2 = 2/6 + 3/6 = 5/6, so the time is 1/(5/6) = 6/5 hours, which is 6/5 x 60 = 72 minutes.
Answer: A
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