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

Question

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

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

Lampard42 · Answer

P1 can drain the full pond in 6 hours.

Rate of P1 (w/t) + Rate of P2 = rate of both together.
1pond in 6 hrs + 1pond in p2 hrs= 1pond in 1 hr(1/2hrs - half pond)
1/6+1/P2=1; so 5P2=6hrs and p2= 1.2 hrs

IMO B

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Ayushpandiya · Answer

what does 'The two pumps working together finish emptying the pond in one-half hour' mean?? 
1. It takes 1/2hr to empty the full tank.
or
2. It takes 1/2hr to empty 1/2 tank. (If this interpretation is correct please explain)

Lampard42 · Answer

Second one is correct as the question says “finish emptying“

Posted from my mobile device

gracie · Answer

in 3 1/2 hours P1 can drain 7/2*1/6=7/12 of pond
so P2 can drain 1-(7/12)=5/12 of pond in one-half hour,
or a rate of 10/12 of pond in one hour
1 pond/(10/12) rate=1.2 hours time for P2 to drain pond alone
B

exc4libur · Answer

rt=j; r_a(3)=0.5 job…r_a=1/6;
(r_a+r_b)(0.5)=0.5 job, r_a+r_b=1, r_b=1-1/6=5/6; 
r_b(t)=1 job…t=1/r_b…t=1/5/6=6/5=1.2 hrs

Answer (B)

LibrarianTurtle · Answer

P1 can drain a 1/2 of a pond in 3h, so rate of P1 is 1/6.
After the P1 drains half of the pond, second pipe (P2) starts to drain the pond as well. 
Let's call the rate of P2 "1/n", since we don't know the time it takes for P2 to drain whole pond.

Together rate of both pipes will be (P1 + P2) -------> 1/6 + 1/n = (n+6)/6n

Together both pipes drain the remaining 1/2 of the pond in 0.5 Hours. So our equation becomes -----> (1/2) / ((n+6)/6n)) = 0.5 
---->6n/(2n+12) = 1/2 ------> 12n = 2n + 12 ------> 10n = 12 ------> n= 12/10 or 6/5.

So rate of P2 becomes 5/6 and the question asks us how long it would take P2 to drain the whole pond on its own. 
(1) / (5/6) -----> 6/5 = 1.2

IMO B

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

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