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

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

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

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

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New post 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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New post 16 Feb 2015, 19:01
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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.

Final Answer:
[Reveal] Spoiler:
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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New post 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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New post 02 Feb 2017, 12:07
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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

Answer: D
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Re: One water pump can fill half of a certain empty tank in 3 hours. Anoth   [#permalink] 02 Feb 2017, 12:07
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