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# One water pump can fill half of a certain empty tank in 3 hours. Anoth

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Intern
Joined: 16 Oct 2011
Posts: 7
Location: Japan
GMAT Date: 03-29-2012
WE: Consulting (Consulting)
One water pump can fill half of a certain empty tank in 3 hours. Anoth  [#permalink]

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04 Jan 2012, 10:17
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Difficulty:

35% (medium)

Question Stats:

73% (01:50) correct 27% (02:08) wrong based on 461 sessions

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One water pump can fill half of a certain empty tank in 3 hours. Another pump can fill half of the same tank in $$3\frac{1}{2}$$ hours. Working together, how long will it take these two pumps to fill the entire tank?

(A) $$1\frac{7}{13}$$

(B) $$1\frac{5}{8}$$

(C) $$3\frac{1}{4}$$

(D) $$3\frac{3}{13}$$

(E) $$3\frac{1}{2}$$
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Re: One water pump can fill half of a certain empty tank in 3 hours. Anoth  [#permalink]

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04 Jan 2012, 10:59
1
36mba wrote:
One water pump can fill half of a certain empty tank in 3 hours. Another pump can fill half of the same tank in $$3\frac{1}{2}$$ hours. Working together, how long will it take these two pumps to fill the entire tank?

(A) $$1\frac{7}{13}$$
(B) $$1\frac{5}{8}$$
(C) $$3\frac{1}{4}$$
(D) $$3\frac{3}{13}$$
(E) $$3\frac{1}{2}$$

One pump can fill a tank in 3 hours and another in 3.5 hours
so the rate at which both can half fill the tank is (1/3+1/3.5) => 13/21

Thus half of the tank can be filled in 21/13

so for filling the complete tank => 21/13*2 = 42/13 (D)
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Re: One water pump can fill half of a certain empty tank in 3 hours. Anoth  [#permalink]

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04 Jan 2012, 11:02
1st pump takes (3+3)=6 hours to fill the full tank
2nd pump takes (3.5+3.5)=7 hours to fill the full tank
Therefore, 1/6 + 1/7= 1/T [T= time it will take if they work together to fill the tank]
solving for T= 3 3/13=D
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Joined: 29 Jul 2011
Posts: 72
Location: United States
Re: One water pump can fill half of a certain empty tank in 3 hours. Anoth  [#permalink]

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04 Jan 2012, 11:45
2
1st pump, 1/2 tank -> 3 hours, full -> 6 hours. This implies rate of 1/6 tank/hr
2nd pump, 1/2 tank -> 3.5 hours, full -> 7 hours. This implies rate of 1/7 tank/hr

Combined rate 1/6 + 1/7 = 13/42
For full tank -> 1/(13/42) = 42/13 = 3 3/13 -> D
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Joined: 23 Dec 2014
Posts: 47
Re: One water pump can fill half of a certain empty tank in 3 hours. Anoth  [#permalink]

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16 Feb 2015, 12:20
36mba wrote:
One water pump can fill half of a certain empty tank in 3 hours. Another pump can fill half of the same tank in $$3\frac{1}{2}$$ hours. Working together, how long will it take these two pumps to fill the entire tank?

(A) $$1\frac{7}{13}$$

(B) $$1\frac{5}{8}$$

(C) $$3\frac{1}{4}$$

(D) $$3\frac{3}{13}$$

(E) $$3\frac{1}{2}$$

1/A = .5/3

1/B = .5/ 3.5

1/A+1/B = .5/3+.5/3.5 = 1/6+1/7 = 13/42

so rate is 13/42
Work =1
Time = 1/ (13/42) = 42/13
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Re: One water pump can fill half of a certain empty tank in 3 hours. Anoth  [#permalink]

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16 Feb 2015, 19:01
1
1
Hi All,

This question is an example of a "Work Formula" question; since it involves just two entities (in this case, water pumps), we can us the Work Formula to quickly get to the correct answer.

We're told that 2 different water pumps can fill HALF of a tank in 3 hours and 3.5 hours, respectively. That means that the two pumps could fill the ENTIRE tank in 6 hours and 7 hours, respectively.

Work = (A)(B)/(A+B)

A = 6 hours
B = 7 hours

(6)(7)/(6+7) = 42/13 = 3 3/13 hours to fill the entire tank when working together.

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Re: One water pump can fill half of a certain empty tank in 3 hours. Anoth  [#permalink]

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30 Jan 2017, 04:05
1) First we need to find the rates of each pump individually: $$r*t=w, r1*3=1/2, r1=1/2*1/3=1/6; r2*7/2=1/2, r2=1/2*2/7=1/7$$.
2) Then we need to combine the two rates, since the pumps are working simultaneously: $$1/6+1/7=13/42$$
3) Now we can find the time it takes the two of them to fill the tank: $$13/42*T=1$$; $$T=42/13=3 \frac{3}{13}$$
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Re: One water pump can fill half of a certain empty tank in 3 hours. Anoth  [#permalink]

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02 Feb 2017, 12:07
36mba wrote:
One water pump can fill half of a certain empty tank in 3 hours. Another pump can fill half of the same tank in $$3\frac{1}{2}$$ hours. Working together, how long will it take these two pumps to fill the entire tank?

(A) $$1\frac{7}{13}$$

(B) $$1\frac{5}{8}$$

(C) $$3\frac{1}{4}$$

(D) $$3\frac{3}{13}$$

(E) $$3\frac{1}{2}$$

We are given that a water pump can fill half of a certain tank in 3 hours; thus, the rate of the pump is (1/2)/3 = 1/6. We are given that another pump can fill 1/2 of the same tank in 3½, or 7/2, hours. Thus, the rate of the second pump is (1/2)/(7/2) = 2/14 = 1/7. If we let t = the time it takes the two pumps working together to fill the entire tank, and if we let 1 equal the work (i.e., filling the entire tank) needed to be completed, we can create the following equation and determine t:

(1/6)t + (1/7)t = 1

Multiplying the entire equation by 42, we have:

7t + 6t = 42

13t = 42

t = 42/13 = 3 3/13

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Re: One water pump can fill half of a certain empty tank in 3 hours. Anoth  [#permalink]

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16 Nov 2019, 16:13
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Re: One water pump can fill half of a certain empty tank in 3 hours. Anoth   [#permalink] 16 Nov 2019, 16:13
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