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

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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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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 hours
C. 3 hours
D. 5 hours
E. 6 hours
[Reveal] Spoiler: OA

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Joined: 24 Apr 2016
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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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New post 21 Apr 2017, 00:37
Rate at which First Pump drains = P1
Rate at which Second Pump drains = P2

Given

(1/P1) * 3 = W/2 [ W here represents the complete work of draining the pond] -- Equation 1

1/P1 = W/6 --> Substituting this in Equation 1

(1/P1 + 1/P2) * 1/2 = W/2 -- Equation 2

W/6 + 1/P2 = W
1/P2 = 5W/6

1/P2 * 6/5 = W

Therefore the second pump will take 6/5 hr or 1.2 hrs to drain the pond on it's own.

Answer is B. 1.2 hours
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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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New post 21 Apr 2017, 02:22
given pump drains one half in 3 hrs,,so full in 6 hrs... also half of the work is done. so half left
rate of one pump is 1/6..
let x be the time taken by the second pump to empty the pond
rate of second pump is 1/x ..

to complete second half of the work,
rate * time = work

(1/6 + 1/x) * 1/2 = 1/2

solve for x = 6/5 = 1.2 hrs,,
ans B
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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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New post 21 Apr 2017, 09:56
Bunuel wrote:
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 hours
C. 3 hours
D. 5 hours
E. 6 hours


rate of p1=1/6
rate of p2=x
1/2(1/6+x)=1/2
x=5/6
6/5=1.2 hours
B
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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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New post 25 Apr 2017, 06:51
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Bunuel wrote:
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 hours
C. 3 hours
D. 5 hours
E. 6 hours


We are given that one pump drains one-half of a pond in three hours. Thus, the rate of that pump is (1/2)/3 = 1/6. When the second pump starts helping to empty the remainder of the pond, i.e., half of the pond, we can let x = the time for the second pump to empty the pond alone. Thus, the rate of the second pump = 1/x. We use the formula for work, work = rate x time, to create the following equation:

(1/6)(1/2) + (1/x)(1/2) = 1/2

1/6 + 1/x = 1

Multiplying the entire equation by 6x, we have:

x + 6 = 6x

6 = 5x

1.2 = x

Thus, the second pump could drain the pond in 1.2 hours.

Answer: B
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Re: One pump drains one-half of a pond in 3 hours, and then a second pump   [#permalink] 25 Apr 2017, 06:51
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