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Math Expert V
Joined: 02 Sep 2009
Posts: 64216
One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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Difficulty:   15% (low)

Question Stats: 88% (01:53) correct 12% (02:49) wrong based on 97 sessions

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One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3 hours. A second inlet pipe can fill the empty cistern to 3/4 of its capacity in 4.5 hours. If both pipes are opened simultaneously, how long, in hours, will it take to fill the cistern?

(A) 4.75
(B) 4.25
(C) 3.75
(D) 3.6
(E) 3.25

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Math Expert V
Joined: 02 Sep 2009
Posts: 64216
Re: One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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Bunuel wrote:
One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3 hours. A second inlet pipe can fill the empty cistern to 3/4 of its capacity in 4.5 hours. If both pipes are opened simultaneously, how long, in hours, will it take to fill the cistern?

(A) 4.75
(B) 4.25
(C) 3.75
(D) 3.6
(E) 3.25

17. Work/Rate Problems

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GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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Bunuel wrote:
One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3 hours. A second inlet pipe can fill the empty cistern to 3/4 of its capacity in 4.5 hours. If both pipes are opened simultaneously, how long, in hours, will it take to fill the cistern?

(A) 4.75
(B) 4.25
(C) 3.75
(D) 3.6
(E) 3.25

IMO D.

First pipe fills 1/3rd cistern in 3 hours. So whole cistern in 9 hours. Therefor it's rate = 1/9 cistern per hour.
Second pipe fills 3/4th cistern in 4.5 hours.

So it fills 1 cistern in 4.5 * 4/3 = 6 hours. Rate of second pipe = 1/6 cistern per hour

When working together rates will add up.

together rate = 1/6 + 1/9
=3/18 + 2/18
=5/18 cistern in one hour

Hence 1 cistern in 18/5 hours or 3.6 hrs

Hence Option D.

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Senior SC Moderator V
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One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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Bunuel wrote:
One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3 hours. A second inlet pipe can fill the empty cistern to 3/4 of its capacity in 4.5 hours. If both pipes are opened simultaneously, how long, in hours, will it take to fill the cistern?

(A) 4.75
(B) 4.25
(C) 3.75
(D) 3.6
(E) 3.25

Pipe 1 rate: $$\frac{(\frac{1}{3})}{3}=(\frac{1}{3}*\frac{1}{3})=\frac{1}{9}$$

Pipe 2 rate: $$\frac{\frac{3}{4}}{\frac{9}{2}}=(\frac{3}{4}*\frac{2}{9})=\frac{1}{6}$$

Together, combined rate is
$$(\frac{1}{9}+\frac{1}{6})=\frac{15}{54}=\frac{5}{18}$$

W = 1 (cistern)
Rate and time are inversely proportional, and here, multiplied, they must equal 1.

Flip the rate to get the time, in hours, that it would take to fill the cistern*:
$$\frac{18}{5}= 3.6$$ hours

*OR
$$R*T = W$$, so $$T=\frac{W}{R}$$
$$T = \frac{1}{(\frac{5}{18})}= (1* \frac{18}{5})=3.6$$ hours

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Re: One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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Bunuel wrote:
One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3 hours. A second inlet pipe can fill the empty cistern to 3/4 of its capacity in 4.5 hours. If both pipes are opened simultaneously, how long, in hours, will it take to fill the cistern?

(A) 4.75
(B) 4.25
(C) 3.75
(D) 3.6
(E) 3.25
First inlet pipe can fill the empty cistern in 9 hours and the second inlet pipe can fill the cistern in 6 hours.

Let the total capacity of the Cistern be 18 units.

So, Efficiency of the First Inlet pipe is 2 units/hour and efficiency of the Second inlet pipe is 3 units/hour

Combined efficiency of both the pipes is 5 units /hour, thus working together the 2 machines can fill the cistern in $$\frac{18}{5}$$ = $$3.6$$ hours, Answer must be (D)
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Re: One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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Bunuel wrote:
One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3 hours. A second inlet pipe can fill the empty cistern to 3/4 of its capacity in 4.5 hours. If both pipes are opened simultaneously, how long, in hours, will it take to fill the cistern?

(A) 4.75
(B) 4.25
(C) 3.75
(D) 3.6
(E) 3.25

We see that the first pipe has a rate of (1/3)/3 = 1/9 and the second pipe has a rate of (3/4)/4.5 = (3/4)/(9/2) = 3/4 x 2/9 = 1/6. Let t = the time, in hours, it takes for both pipes work together to fill the cistern, we can create the equation:

t(1/9 + 1/6) = 1

t(2/18 + 3/18) = 1

t(5/18) = 1

t = 18/5 = 3.6

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Re: One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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This is a fairly simple question on rates. At your peak, you should be able to solve this question in less than a minute.

If the first inlet pipe can fill $$\frac{1}{3}$$rd of an empty cistern in 3 hours, we can conclude that it can fill the whole cistern in 9 hours.

Similarly, if the second inlet pipe can fill $$\frac{3}{4}$$th of the cistern in 4.5 hours, it can fill the whole cistern in 6 hours.

Let us assume the volume of the cistern to be 18 gallons, which is the LCM of 9 and 6. This represents the work to be done by the inlet pipes.

The first pipe can fill 18 gallons in 9 hours, so it fills at the rate of 2 gallons per hour. We can conclude similarly, that the second pipe fills at the rate of 3 gallons per hour.
If they are opened simultaneously, they can fill 5 gallons per hour.

At this rate, they will take

$$\frac{18}{5}$$ = 3.6 hours to fill the entire cistern.

The correct answer option is D.

Hope this helps!
_________________ Re: One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3   [#permalink] 04 Jun 2019, 07:28

# One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  