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Difficulty: Sub 505 Level,   Work and Rate Problems,                           
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Re: One inlet pipe fills an empty tank in 5 hours. A second inle [#permalink]
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This equation comes in handy


\(W=\frac{AB}{A+B}\) where A and B are rates and W is the work done.

A=3; B=5
\(W=\frac{15}{8}\)

To complete 2/3 of the work \(= \frac{2}{3}*\frac{15}{8} = \frac{5}{4}\)
Answer is C
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Re: One inlet pipe fills an empty tank in 5 hours. A second inle [#permalink]
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Hi All,

Since we have two 'entities' working on a task together, this is essentially just a Work Formula question. It does come with a minor 'twist' though.

Work = (A)(B)/(A+B) where A and B are the individual times to complete the task

The two pipes can fill the tank in 5 hours and 3 hours, respectively. Working together, it would take...

(5)(3)/(5+3) = 15/8 hours to fill the ENTIRE tank.

We're asked how long it would take to fill 2/3 of the tank, so we have to multiply the above number by 2/3...

(15/8)(2/3) = 30/24 = 5/4 hours

Final Answer:

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Re: One inlet pipe fills an empty tank in 5 hours. A second inle [#permalink]
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Quote:
One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill 2/3 of the tank?

(A) 8/15 hr
(B) 3/4 hr
(C) 5/4 hr
(D) 15/8 hr
(E) 8/3 hr


The combined rate of the pipes is 1/5 + 1/3 = 3/15 + 5/15 = 8/15.

If we let n = the time if takes to fill the 2/3 of the tank, then:

(8/15)n = 2/3

Multiplying by 15, we have:

8n = 10

n = 10/8 = 5/4 hours

Answer: C
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Re: One inlet pipe fills an empty tank in 5 hours. A second inle [#permalink]
VeritasKarishma can you please solve this question by using relative rate concept?

In https://gmatclub.com/forum/veritas-prep ... l#p1562884 the rates of inlet and outlet pipes were added similar to distance rate concept but here the pipes are both inlet and still rates are added. Can you please clarify this doubt?
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Re: One inlet pipe fills an empty tank in 5 hours. A second inle [#permalink]
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Suneha123 wrote:
VeritasKarishma can you please solve this question by using relative rate concept?

In https://gmatclub.com/forum/veritas-prep ... l#p1562884 the rates of inlet and outlet pipes were added similar to distance rate concept but here the pipes are both inlet and still rates are added. Can you please clarify this doubt?


Suneha123

When two things contribute to the same work, their rates get added.
When one makes but the other breaks i.e. they are working towards opposite goals, their rate is subtracted.

In this question, both are working toward filling an empty tank. So their goal is the same. So their rates will get added.

In the question you mentioned in the link, the goal is to have equal amounts of water in the two tanks. Both are working toward it (X by removing water in one tank and Y by adding water to the other tank so that both tanks have equal water). That is why their rates are added too.

When the goal is to fill a tank and one pipe pumps water in the tank but the other pipe removes water from the same tank, that is when they are working in opposite directions. One pipe wants to fill the tank while the other wants to empty it. That is when their rates are subtracted if we want to find the time taken to fill the tank. The other pipe is working against the goal in that case.
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Re: One inlet pipe fills an empty tank in 5 hours. A second inle [#permalink]
Let's denote the rate of the first inlet pipe as R1 (in units of tank per hour) and the rate of the second inlet pipe as R2.

From the problem, we know that R1 = 1/5 (since it takes 5 hours for the first inlet pipe to fill the tank) and R2 = 1/3 (since it takes 3 hours for the second inlet pipe to fill the tank).

When both pipes are used together, their rates add up:

R1 + R2 = 1/5 + 1/3 = 8/15

Therefore, the combined pipes can fill the tank at a rate of 8/15 tank per hour.

To find how long it takes to fill 2/3 of the tank using both pipes, we can use the formula:

time = amount of work / rate

Since the amount of work is 2/3 of a tank and the combined rate of the pipes is 8/15 tank per hour, we have:

time = (2/3) / (8/15) = (2/3) * (15/8) = 5/4

Therefore, it will take 5/4 hours (or 1 hour and 15 minutes) to fill 2/3 of the tank using both pipes.

The answer is (C) 5/4 hr.
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Re: One inlet pipe fills an empty tank in 5 hours. A second inle [#permalink]
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