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# One pump drains one-half of a pond in 3 hours, and then a second pump

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Intern
Joined: 27 Aug 2011
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One pump drains one-half of a pond in 3 hours, and then a second pump  [#permalink]

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Updated on: 27 Jan 2016, 10:22
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Difficulty:

75% (hard)

Question Stats:

53% (02:05) correct 47% (02:15) wrong based on 142 sessions

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One pump drains one-half of a pond in 3 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?

A. 1 hour
B. 1.2 hour
C. 3 hours
D. 5 hours
E. 6 hours

Originally posted by saumzi on 16 Oct 2011, 09:55.
Last edited by Bunuel on 27 Jan 2016, 10:22, edited 1 time in total.
Renamed the topic and edited the question.
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Re: One pump drains one-half of a pond in 3 hours, and then a second pump  [#permalink]

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16 Oct 2011, 10:56
saumzi wrote:
i know its terribly easy but still i m stuck somewhere...

One pump drains one-half of a pond in 3 hours, and then a second pump starts draining the pond.The two pumps working together finish emptying the pond in one-half hour.How long would it take the second pump to drain the pond if it had to do the job alone???

A.1 hour
B.1.2 hour
C.3 hours
D.5 hours
E.6 hours

Can you please check the question? I am getting the answer which is not in option.

Pump 1 drains half of the pond in 3 hrs ==>it will take 6hrs for Pump 1 to drain the entire pond.
Number of hrs taken by pump 2 = Y
If both pumps working together will empty the pond in 1.5hrs==>3/2
==>1/6 + 1/Y = 2/3
==>1/Y = 2/3-1/6 ==>(4-1)/6 =1/2
Y =2
Number of hrs taken by Pump 2 to drain the entire pond = 2hrs
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Re: One pump drains one-half of a pond in 3 hours, and then a second pump  [#permalink]

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16 Oct 2011, 12:26
1/6 + 1/Tb = 1/1.5
1/6 + 1/Tb= 2/3
solving for Tb= 2 hrs
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Re: One pump drains one-half of a pond in 3 hours, and then a second pump  [#permalink]

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27 Jan 2016, 10:17
1
saumzi wrote:
i know its terribly easy but still i m stuck somewhere...

One pump drains one-half of a pond in 3 hours, and then a second pump starts draining the pond.The two pumps working together finish emptying the pond in one-half hour.How long would it take the second pump to drain the pond if it had to do the job alone???

A.1 hour
B.1.2 hour
C.3 hours
D.5 hours
E.6 hours

The tricky part here, I believed is one half hour = 1/2. Then everything would be easy.

We have the 1st pump working rate/hour = 1/2 : 3 = 1/6
Working rate of 2 pumps: 1/2 : 1/2 = 1.
Working rate of 2nd pump: 1 -1/6 = 5/6 --> Time taken for the 2nd pump to finish: 1 : 5/6 = 6/5 = 1.2 hours.
Hope it help
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Re: One pump drains one-half of a pond in 3 hours, and then a second pump  [#permalink]

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27 Jan 2016, 20:04
First pump drains 1/2 of the tank in 3 hours
so 6 hours it will take to drain the full tank.
Let, 2nd pump drains the full tank in a hours
so both together can drain (1/6+1/a) part in 1 hour
son in 1/2 hour they drain 1/2*(1/6+1/a) part of the tank
given that in 1/2 hour they drain 1/2 of the tank
hence we can say
1/2*(1/6+1/a) = 1/2
solving u get a = 6/5=1.2
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One pump drains one-half of a pond in 3 hours, and then a second pump  [#permalink]

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17 Feb 2016, 15:48
if pump 1 drains 1/12 of pond in 1/2 hour,
then pump 2 must drain 1/2-1/12=5/12 of pond in 1/2 hour
let t=pump 2's time to drain entire pond alone
(5/12)/(1/2))=1/t
t=1.2 hours
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One pump drains one-half of a pond in 3 hours, and then a second pump  [#permalink]

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04 Mar 2016, 20:58
rate of pump 1=1/6
rate of pump 1+pump 2=1
rate of pump 2=1-(1/6)=5/6
inverting, 6/5=1.2 hours for pump 2 to drain pond alone
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Re: One pump drains one-half of a pond in 3 hours, and then a second pump  [#permalink]

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13 Aug 2017, 19:48
Let the total capacity of pond be 6.
Pump 1 drains 3 in 3 hrs, i.e. 1 per hour
both pumps finishes draining remaining 3 in 0.5 hour, i.e 6 per hour
Thus rate of pump 2 has to be (total rate - rate of pump 1) = (6-1) = 5 per hour
Pump 2 needs to drain complete 6 @ 5 per hour so time taken is $$\frac{6}{5}$$ = 1.2 hrs
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Re: One pump drains one-half of a pond in 3 hours, and then a second pump  [#permalink]

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13 Aug 2017, 19:55
performance of the first pomp 1/6
then 1/6*1/2+x*1/2=1/2 (half of the pound)

1/12 +x/2 = 1/2
x/2=5/12
12x= 10
x =10/12
so the performance of the second pomp is 5/6

then if the first one has performance of 1/6 and drains the pound in 6 hours, then the second will do that in 6/5 = 1.2h
Re: One pump drains one-half of a pond in 3 hours, and then a second pump   [#permalink] 13 Aug 2017, 19:55
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