When water is flowing into a certain pool at the rate of r gallons per

Question

When water is flowing into a certain pool at the rate of r gallons per hour, it takes 9 hours to fill the pool. In terms of r, how many hours will it take to fill the pool if water is flowing into the pool at the rate of r + 5 gallons per hour?

A. \(\frac{9(r + 5)}{r}\)

B. \(\frac{r + 5}{9r}\)

C. \(\frac{r}{r + 5}\)

D. \(\frac{9r}{r + 5}\)

E. \(\frac{r}{9(r + 5)}\)

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Official Answer

D

Bunuel · Accepted Answer

The capacity of the tank is given by the formula (time)(rate) = 9r gallons.

To fill a pool with a capacity of 9r gallons at a rate of r + 5 gallons per hour, the time required can be calculated using (time) = (capacity)/(rate). Therefore, it takes 9r/(r + 5) hours to fill the pool.

Answer: D.

Archit3110 · Answer

Volume of the pool is 9r
with flow rate of r+5 
the time it will take is 
 \frac{9r}{r + 5} 
option D

Confide · Answer

R*T = W
r*9 = 9r

then
(r+5) * t = 9r
t = 9r/r+5

Abhishek009 · Answer

Total Capacity of the Pool is  9*r =9r

Increased efficiency of the Pipe is (r + 5)

So, Time required to fill the Pool will be  \frac{9r}{(r+5)} , Answer must be (D)

Calista_Pro · Answer

Hi, I understand why D is correct, but not I don't get why A is wrong, as my first reflex was to do a cross calculation. Why is it wrong in that case? There is no proportionnality?

MartyMurray · Answer

You can think of it this way.

Logically, when the rate increases from r to r + 5, the number of hours it takes for the pool to be filled should decrease.

However, the choice (A) value,  \frac{9(r + 5)}{r} , is greater than 9 since  \frac{(r + 5)}{r} > 1 .

So, (A) doesn't make sense because it would mean that the number of hours increases rather than decreases when the rate increases.

When water is flowing into a certain pool at the rate of r gallons per

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When water is flowing into a certain pool at the rate of r gallons per

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