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

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

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

by BTGmoderatorRO » Sun Mar 25, 2018 9:12 am

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

Please, I want experts to help me with the approach to solve this question.
Thanks

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Source: Beat The GMAT — Problem Solving | Sun Mar 25, 2018 9:12 am

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by [email protected] » Sun Mar 25, 2018 2:45 pm

Hi Roland2rule,

We're told that one inlet pipe can fill an empty cistern to 1/3 of its capacity in 3 hours and a second inlet pipe can fill the empty cistern to 3/4 of its capacity in 4.5 hours. We're asked how long (in hours) it would take to fill the cistern. Since we have two 'entities' working on a task together, this is essentially just a Work Formula question.

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

Since the first inlet pipe can fill an empty cistern to 1/3 of its capacity in 3 hours, it can fill the ENTIRE cistern in 9 hours.
Since the second inlet pipe can fill the empty cistern to 3/4 of its capacity in 4.5 hours, it can fill the ENTIRE cistern in (4/3)(9/2) = 36/6 = 6 hours.

Working together, it would take....

(9)(6)/(9+6) = 54/15 = 3 9/15 = 3 3/5 = 3.6 hours to fill the ENTIRE tank.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Fri May 24, 2019 1:19 pm

BTGmoderatorRO 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

Answer: D

Scott Woodbury-Stewart
Founder and CEO
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