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

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Math Expert
Joined: 02 Sep 2009
Posts: 47157
One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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20 Mar 2018, 23:03
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15% (low)

Question Stats:

95% (01:32) correct 5% (03:14) wrong based on 75 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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Posts: 47157
Re: One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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20 Mar 2018, 23:04
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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Re: One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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21 Mar 2018, 01:00
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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One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3  [#permalink]

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23 Mar 2018, 22:33
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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24 Mar 2018, 07:43
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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Abhishek....

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Re: One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3 &nbs [#permalink] 24 Mar 2018, 07:43
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