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An empty swimming pool can be filled by two hoses. Hose A can fill it in 6 hours and hose B can fill it in 8 hours. How many hours will it take to fill the swimming pool if both hoses are used simultaneously?

I tried this problem, but I don't know if it looks correct.

$V = 6 v_A$

$V = 8 v_B$

$V = (v_A + v_B) t$

$V = \left( \frac{V}{6} + \frac{V}{8} \right) t$

$V = \frac{4V + 3V}{24} t$

$1 = \frac{7}{24} t$

$t = \frac{24}{7}$

$t \approx 3.4285 \ldots$

The question is multiple choice.

a) 3.1

b) 3.2

c) 3.3

d) 3.4

e) none of these

It seems that, from what I calculated, the answer should be (e). But I am not too sure if I calculated it correctly.

Jason Chiu
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    $24/7$ looks right to me. I would answer d) on the test, but who knows? – saulspatz Mar 17 '20 at 16:06
  • This is a typical example of Harmonic Mean, and indeed, the answer is 24/7 – imranfat Mar 17 '20 at 16:33
  • Check the instructions on the question or problem set. Does it discuss rounding? If there was no mention of rounding anywhere in the instructions, Then I would say that (d) and (e) should both be considered correct. If the instructions do meantion rounding, then (d) alone will be correct. Of course even when rounding was not mentioned, that could be simply because the instructor forgot to meantion it, or was lazy and just assumed you'd understand. – Paul Sinclair Mar 18 '20 at 00:34

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