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Two pipes A and B fill a swimming pool at constant rates of 10 gallons

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Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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New post 22 Mar 2019, 05:55
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A
B
C
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E

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
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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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New post 22 Mar 2019, 07:55
1
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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Re: Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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New post 22 Mar 2019, 08:36
chetan2u why did you equate it to 1

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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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New post 22 Mar 2019, 08:41
btrg wrote:
chetan2u why did you equate it to 1

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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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Re: Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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New post 24 Mar 2019, 18:28
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.

Answer: B
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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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New post 05 Apr 2019, 06:21
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.
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Two pipes A and B fill a swimming pool at constant rates of 10 gallons  [#permalink]

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New post 07 Apr 2019, 17:53
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
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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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Two pipes A and B fill a swimming pool at constant rates of 10 gallons

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