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

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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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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
[Reveal] Spoiler: OA

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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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New post 20 Mar 2018, 23:04
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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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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New post 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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New post 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

ANSWER D

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