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# Two different pumps are used to fill an empty water tank. The first pu

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Math Expert
Joined: 02 Sep 2009
Posts: 64101
Two different pumps are used to fill an empty water tank. The first pu  [#permalink]

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17 May 2017, 23:26
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Difficulty:

65% (hard)

Question Stats:

66% (02:39) correct 34% (02:54) wrong based on 179 sessions

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Two different pumps are used to fill an empty water tank. The first pump can fill the tank in 24 hours and the second pump works at 2/3 the speed of the first pump. The first pump is used alone for 8 hours and then the second pump is added until the tank is full. How long does it take in total for the empty tank to be filled?

A. 9 hours and 36 minutes
B. 10 hours
C. 11 hours and 12 minutes
D. 17 hours and 36 minutes
E. 18 hours

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Re: Two different pumps are used to fill an empty water tank. The first pu  [#permalink]

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22 May 2017, 17:28
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Bunuel wrote:
Two different pumps are used to fill an empty water tank. The first pump can fill the tank in 24 hours and the second pump works at 2/3 the speed of the first pump. The first pump is used alone for 8 hours and then the second pump is added until the tank is full. How long does it take in total for the empty tank to be filled?

A. 9 hours and 36 minutes
B. 10 hours
C. 11 hours and 12 minutes
D. 17 hours and 36 minutes
E. 18 hours

We are given that the rate of the first pump is 1/24. Since the second pump has a rate that is 2/3 of the first pump, the rate of the second pump is (1/24) x (2/3) = 2/72 = 1/36.

If the first pump is used for 8 hours, 1/24 x 8 = 8/24 = 1/3 of the tank is filled, leaving 2/3 left to be filled.

Since the second pump is then added to complete the job, the combined rate is 1/24 + 1/36 = 3/72 + 2/72 = 5/72. We can let t = the time it takes to complete the job:

(5/72)t = 2/3

5t/72 = 2/3

15t = 144

t = 144/15 = 48/5 = 9 ⅗ hours = 9 hours and 36 minutes

Thus, the tank is filled in 8 hours + 9 hours and 36 minutes = 17 hours and 36 minutes.

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Two different pumps are used to fill an empty water tank. The first pu  [#permalink]

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Updated on: 18 May 2017, 05:53
1
1
Bunuel wrote:
Two different pumps are used to fill an empty water tank. The first pump can fill the tank in 24 hours and the second pump works at 2/3 the speed of the first pump. The first pump is used alone for 8 hours and then the second pump is added until the tank is full. How long does it take in total for the empty tank to be filled?

A. 9 hours and 36 minutes
B. 10 hours
C. 11 hours and 12 minutes
D. 17 hours and 36 minutes
E. 18 hours

First pump time = 24 hours

Second pump time = (3/2)*24 = 36 hours (since speed is 2/3 so the time should be 3/2 times)

Let total time to fill the tank = T

the First pump works for T hours and second pump works for (T-8) Hours

i.e. T/24 + (T-8)/36 = 1

i.e. 3T + 2*(T-8) = 72

i.e. 5T = 88

i.e. T = 17 3/5 hour = 17 hours 36 mins

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Originally posted by GMATinsight on 18 May 2017, 00:51.
Last edited by GMATinsight on 18 May 2017, 05:53, edited 1 time in total.
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Re: Two different pumps are used to fill an empty water tank. The first pu  [#permalink]

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18 May 2017, 04:26
GMATinsight wrote:
Bunuel wrote:
Two different pumps are used to fill an empty water tank. The first pump can fill the tank in 24 hours and the second pump works at 2/3 the speed of the first pump. The first pump is used alone for 8 hours and then the second pump is added until the tank is full. How long does it take in total for the empty tank to be filled?

A. 9 hours and 36 minutes
B. 10 hours
C. 11 hours and 12 minutes
D. 17 hours and 36 minutes
E. 18 hours

First pump time = 24 hours

Second pump time = (3/2)*24 = 36 hours (since speed is 2/3 so the time should be 3/2 times)

Let total time to fill the tank = T

the First pump works for T hours and second pump works for (T-8) Hours

i.e. T/24 + (T-8)/36 = 1

i.e. 3T + 2*(T-8) = 72

i.e. 5T = 56

i.e. T = 11 1/5 hour = 11 hours 12 mins

should be (D) ?
3T + 2*(T-8) = 72
5T = 88
T = 17.6 h = 17 h 36 min
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Re: Two different pumps are used to fill an empty water tank. The first pu  [#permalink]

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16 Apr 2018, 00:39
+1 for option D. The key here is to recognize that if the speed is 2/3 , the time taken becomes 3/2.
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Two different pumps are used to fill an empty water tank. The first pu  [#permalink]

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16 Apr 2018, 17:06
1
Bunuel wrote:
Two different pumps are used to fill an empty water tank. The first pump can fill the tank in 24 hours and the second pump works at 2/3 the speed of the first pump. The first pump is used alone for 8 hours and then the second pump is added until the tank is full. How long does it take in total for the empty tank to be filled?

A. 9 hours and 36 minutes
B. 10 hours
C. 11 hours and 12 minutes
D. 17 hours and 36 minutes
E. 18 hours

If you happen not to see the inverse proportion shortcut, the "long way" is not bad at all. One hitch: at the end add time taken in both stages

Use Stage 1 to find amount of work finished by Pump A working alone. Use Stage 2 to find time for both pumps to finish.

Stage 1: Pump A works alone. Work finished?

Pump A's rate = $$\frac{1}{24}$$
Pump A's time = 8 hours

Work finished by Pump A alone:
$$W=(r*t)= (\frac{1}{24}*8)=\frac{8}{24}=\frac{1}{3}$$
of work is finished
So $$\frac{2}{3}$$ remains.

Stage 2: Pumps A and B work together

Pump A's rate =$$\frac{1}{24}$$

Pump B's rate is $$\frac{2}{3}$$ of A's rate
Pump B's rate: $$(\frac{2}{3}*\frac{1}{24})=\frac{1}{36}$$

Combined rate of A and B:
$$(\frac{1}{24}+\frac{1}{36})=(\frac{3}{72}+\frac{2}{72})=\frac{5}{72}$$

Work, W, remaining = $$\frac{2}{3}$$

Time taken by A and B working together?
Time$$=\frac{W}{r}=\frac{\frac{2}{3}}{\frac{5}{72}}=(\frac{2}{3}*\frac{72}{5})=$$
$$\frac{48}{5}$$ hours

Total time taken to fill the entire tank?
(Stage 1 + Stage 2) = (8 hrs + $$\frac{48}{5}$$ hrs) =
$$(\frac{40}{5}+\frac{48}{5})=\frac{88}{5}=17\frac{3}{5}$$ hours

ANY fraction of an hour * 60 = # of minutes
($$\frac{3}{5}$$ * 60) = 36 minutes

17 hours, 36 minutes

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Re: Two different pumps are used to fill an empty water tank. The first pu  [#permalink]

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05 Aug 2019, 10:04
First pump takes 24hrs.
Second pump works at 2/3 the speed of first, hence it takes 3/2 of the time, i.e.36hrs.
Work done per hour by first pump=1/24
Work done per hour by second pump=1/36
Overall work done per hour=1/24+1/36=5/72.
First pump in 8 hrs filled [8*(1/24)] of the tank, i.e. 1/3rd of the tank.
Time taken to fill remaining 2/3 of tank = (2/3)/(5/72) = 9hrs 36min
Therefore overall time taken = 8hrs + 9hrs36min = 17hours 36 min
Re: Two different pumps are used to fill an empty water tank. The first pu   [#permalink] 05 Aug 2019, 10:04