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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.

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.

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