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It takes h minutes to fill a hot tub with a hot wat

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It takes h minutes to fill a hot tub with a hot wat [#permalink]  22 Aug 2017, 02:23
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81% (01:25) correct 18% (02:14) wrong based on 22 sessions

It takes h minutes to fill a hot tub with a hot water hose and c minutes to fill it with a cold water hose, where c is smaller than h.

 Quantity A Quantity B $$\frac{h^2}{c + h}$$ The number of minutes required to fill the hot tub using the hot water hose and the cold water hose simultaneously

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: It takes h minutes to fill a hot tub with a hot wat [#permalink]  28 Sep 2017, 08:42
The rate for the hot water hose is 1/h, while the one for the cold water hose is 1/c. When they work together we have to sum their rates so that we get a combined rate of $$\frac{c+h}{hc}$$. Given the rate, the minutes necessary to fill the hot tub are $$\frac{hc}{h+c}$$ and, given that c < h, we have that the numerator of column B is smaller while the denominator is the same of column A.

Thus, we can conclude that column A is greater!
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Re: It takes h minutes to fill a hot tub with a hot wat [#permalink]  28 Sep 2017, 12:10
if hot water takes = h mins to fill the tub

and cold water takes= c mins to fill the tub

Therefore working together they can complete in = $$\frac{{h*c}}{{h + c}}$$ mins (This is general formula if we need to calculate the time required if two different individual work together)

Now back to ques, since denominator is same and h>c

Therefore QTY A > QTY B
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Re: It takes h minutes to fill a hot tub with a hot wat   [#permalink] 28 Sep 2017, 12:10
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