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# A draining pipe can empty a pool in 4 hours

tagged by: NandishSS

#### A draining pipe can empty a pool in 4 hours

A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?

A. 9 liters
B. 18 liters
C. 27 liters
D. 36 liters
E. 45 liters

OA: D[/spoiler]

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NandishSS wrote:
A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?

A. 9 liters
B. 18 liters
C. 27 liters
D. 36 liters
E. 45 liters

OA: D[/spoiler]
C = Capacity of the pool in L
R = Rate of drainage in L per hour

Work = Rate * Time
(1) C = R *4 (we know that the pool can be emptied in 4 hours)
(2) C + 3*6 = R*6 (we know that when its raining and an extra 3L is added to the pool an hour the pool is emptied in 6 hours

(1) C = 4R
(2) C + 18 = 6R

4R + 18 = 6R [put equation (1) into (2) to eliminate C]
2R = 18
R = 9

C = 4*9 [Put R = 9 into equation (1) to work out C]
C = 36

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NandishSS wrote:
A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?

A. 9 liters
B. 18 liters
C. 27 liters
D. 36 liters
E. 45 liters
We can PLUG IN THE ANSWERS, which represent the capacity of the pool.
When the correct answer is plugged in, the time to empty the pool when the draining pipe and intake pipe work simultaneously = 6 hours.
The correct answer is likely to be divisible by the given times and rates (4 hours, 6 hours, 3 liters per hour).
Only D is a multiple of 4, 6 and 3.

D: 36 liters
Since the draining pipe alone takes 4 hours hours to drain the pool, the draining pipe's rate = w/t = 36/4 = 9 liters per hour.
Since the draining pipe REMOVES 9 liters per hour, while the intake pipe ADDS 3 liters per hour, the net removal rate when the two pipes operate together = 9-3 = 6 liters per hour.
Since the two pipes together have a net removal rate of 6 liters per hour, the time for the two pipes together to empty the 36-liter pool = w/r = 36/6 = 6 hours.
Success!

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NandishSS wrote:
A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?

A. 9 liters
B. 18 liters
C. 27 liters
D. 36 liters
E. 45 liters
We can let c = the capacity of the pool. We see that the rate of the pipe emptying the pool is c/4 when the pool is full and itâ€™s not raining. and that the rate of the pipe emptying the pool is c/6 when the pool is full and itâ€™s raining. We can create the following equation:

c/4 - 3 = c/6

Multiplying the equation by 12, we have:

3c - 36 = 2c

c = 36

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Jeffrey Miller Head of GMAT Instruction

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Hi NandishSS,

Let the rate of the draining pipe be xx liters per hour. Then the capacity of the tank will be C = time âˆ- rate = 4x.

Now, when raining, the net outflow is x-3 liters per hour, and we are told that at this new rate the pool is emptied in 6 hours.

So, the capacity of the pool also equals to C = time âˆ- rate = 6(x-3).

Thus we have: 4x = 6(x-3) --> x = 9 --> C = 4x = 36. Option D.

Regards!

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