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Manager  S
Joined: 31 Oct 2018
Posts: 77
Location: India
Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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2 00:00

Difficulty:   65% (hard)

Question Stats: 58% (02:39) correct 42% (03:12) wrong based on 38 sessions

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Two pipes A and B fill a swimming pool at constant rates of 10 gallons per minute and 15 gallons per minute respectively. The pool can be filled in 60 hours if Pipe A alone is left open or 40 hours if Pipe B alone is left open or 24 hours if both pipes are left open. If pipe B alone is used for half of the time to fill the pool and then both the pipes are used for remaining time, how many hours does it take to fill the pool?

A. 15
B. 30
C. 38.7
D. 42
E. 50

OA
Math Expert V
Joined: 02 Aug 2009
Posts: 8320
Re: Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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btrg wrote:
Two pipes A and B fill a swimming pool at constant rates of 10 gallons per minute and 15 gallons per minute respectively. The pool can be filled in 60 hours if Pipe A alone is left open or 40 hours if Pipe B alone is left open or 24 hours if both pipes are left open. If pipe B alone is used for half of the time to fill the pool and then both the pipes are used for remaining time, how many hours does it take to fill the pool?

A. 15
B. 30
C. 38.7
D. 42
E. 50

OA

You dont require the speed, just time is sufficient.

Let the time taken be 2x. so B works for entire duration 2x and A works for half duration x...
$$\frac{x}{60}+\frac{2x}{40}=1.....\frac{2x+6x}{120}=1........8x=120.......x=15.....2x=30.$$

we could have made the equation as
Let the time taken be 2x. so B works alone for x and both combined work for half duration x...
$$\frac{x}{40}+\frac{x}{24}=1.....\frac{3x+5x}{120}=1........8x=120.......x=15.....2x=30.$$

B
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Manager  S
Joined: 31 Oct 2018
Posts: 77
Location: India
Re: Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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chetan2u why did you equate it to 1

Posted from my mobile device
Math Expert V
Joined: 02 Aug 2009
Posts: 8320
Re: Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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btrg wrote:
chetan2u why did you equate it to 1

Posted from my mobile device

Hi,
1/24 is the fraction of work done in 1 hour, if the work is done in 24 hours..
So in x hours x/24 part of the work will be done
Similarly x/40 part of the work will be done by B alone in x hours.
Thus the combinations should be 1, that represents ONE complete work.

That is why x/24 + x/40 =1
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Target Test Prep Representative V
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Re: Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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btrg wrote:
Two pipes A and B fill a swimming pool at constant rates of 10 gallons per minute and 15 gallons per minute respectively. The pool can be filled in 60 hours if Pipe A alone is left open or 40 hours if Pipe B alone is left open or 24 hours if both pipes are left open. If pipe B alone is used for half of the time to fill the pool and then both the pipes are used for remaining time, how many hours does it take to fill the pool?

A. 15
B. 30
C. 38.7
D. 42
E. 50

OA

We see that the capacity of the pool is 10 x 60 = 600 (or 15 x 40 = 600) gallons. If pipe B is used for half the time to fill the pool, we can let n = the time, in hours, pipe A has filled the pool after pipe B has filled the pool for the same amount of time, thus pipe B’s time = 2n and we can create the equation:

15(2n) + 10n = 600

40n = 600

n = 15

So the total time is 2 x 15 = 30 hours.

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Manager  S
Joined: 11 Jun 2018
Posts: 130
GMAT 1: 500 Q39 V21 Re: Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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2
When A works alone= 10 Gallon/Min * 3600 minutes = 36000
When B works alone= 15 Gallon/Min *2400 Minutes = 36000
When A + B Work= 25 Gallon/Min *1440 minutes = 36000

Now, B works alone for half the time and A+B work together for the remaining half
Assume time to be X
15 G/Min * (X/2) + 25 G/Min * (X/2)= 36000
(15X)/2+(25X)/2= 36000
(15X+25X)/2 =36000
40X=72000
X=1800

Convert into Hours 1800/60= 30 Hours.
VP  P
Joined: 07 Dec 2014
Posts: 1217
Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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Two pipes A and B fill a swimming pool at constant rates of 10 gallons per minute and 15 gallons per minute respectively. The pool can be filled in 60 hours if Pipe A alone is left open or 40 hours if Pipe B alone is left open or 24 hours if both pipes are left open. If pipe B alone is used for half of the time to fill the pool and then both the pipes are used for remaining time, how many hours does it take to fill the pool?

A. 15
B. 30
C. 38.7
D. 42
E. 50

let t=hours to fill pool
t/2*(1/40+1/24)=1➡
t=30 hours
B Two pipes A and B fill a swimming pool at constant rates of 10 gallons   [#permalink] 07 Apr 2019, 17:53
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