Two pipes A and B fill a swimming pool at constant rates of 10 gallons

Question

Two pipes A and B fill a swimming pool at constant rates of 10 gallons per minute and 15 gallons per minute respectively. The pool can be filled in 60 hours if Pipe A alone is left open or 40 hours if Pipe B alone is left open or 24 hours if both pipes are left open. If pipe B alone is used for half of the time to fill the pool and then both the pipes are used for remaining time, how many hours does it take to fill the pool?

A. 15
B. 30
C. 38.7
D. 42
E. 50

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tgsankar10 · Answer

Rate of Pipe A  =10\frac{g}{min}=600\frac{g}{hr}

Rate of Pipe B  =15\frac{g}{min}=900\frac{g}{hr}

Capacity of pool  =	ext{Rate of A * Time taken by A}=600*60=36000	ext{ gallons}

Rate of Pipe A & B  =\frac{	ext{Work Done}}{	ext{Time taken}}=\frac{36000}{24}=1500\frac{g}{hr}

ext{Rate of B}*\frac{t}{2}+	ext{Rate of A & B}*\frac{t}{2}=36000

900t+1500t=72000

t=\frac{72000}{2400}=30

Answer is B

Krunaal · Answer

Pipe A

Rate = 10 gallons / minute => 600 gallons / hour
Time taken alone to fill the pool = 60 hours

Pipe B

Rate = 15 gallons / minute => 900 gallons / hour
Time taken alone to fill the pool = 40 hours

Together

Rate = 1500 gallons / hour
Time taken alone to fill the pool = 24 hours

From above we can infer that total capacity of pool is 36000 gallons

Total Work done = Total Rate of work * Total Time taken

We are given that pipe B was used alone for half of the total time and for the remaining time both pipes were used,

Total Work done = Rate of work of pipe B alone * (Total Time / 2) + Rate of work of both pipes together * (Total Time / 2)
36000 = 900 * (T/2) + 1500 * (T/2)
36000 = 1200 * T
T = 30

Therefore Total Time taken to fill the pool = Answer B.) 30 hours

Nidzo · Answer

To fill the pool Pipe A takes 60h, Pipe B takes 40h and together it takes them 24h. What one is not given is the amount of water the pool can hold. However, one can assign a value as long as it works will three times. In this instance, one can see that 60, 40 and 24 all go into 120.

Let the amount of water the pool can hold =  120 l.

This means that Pipe A has a rate of  2 l an hour, Pipe B has a rate of  3 l and hour and together they have a rate of  5 l an hour.

Pipe B alone is used for half of the time to fill the pool and then both the pipes are used for remaining time:

One is told that half the time Pipe B works alone and the other half of the time both A and B work together. Let the total time spent filling the pool =  2x .

Pipe B alone:  Pumping  3 l an hour for  x  hours means that Pipe B will pump  3x l alone.

Pipe A & B together:  Pumping  5 l an hour for  x  hours means that together they will pump  5x l.

Time it took to fill the pool:  In total, the pool was filled with  5x l of water in a time frame of  2x  hours.

One knows that the pool is 120l, and therefore:

8x = 120   divide through by 4 to find the answer for 2x]

2x = 30

ANSWER B

mcrea · Answer

I do not know how much GMAT-like this question is... too much useless information.
You literaly just need "40 hours if Pipe B alone is left open or 24 hours if both pipes are left open"

t * (1/40 * 1/2 + 1/24 * 1/2) = 1
solve and get t=30

Two pipes A and B fill a swimming pool at constant rates of 10 gallons

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GMAT Problem Solving (PS) Questions

Two pipes A and B fill a swimming pool at constant rates of 10 gallons

Prep Toolkit

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