SOLUTION: A pond is being drained by a pump. After 3 hours, the pond is half empty. A second pump is put into operation, and together the two pumps finish emptying the pond in half an hour.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A pond is being drained by a pump. After 3 hours, the pond is half empty. A second pump is put into operation, and together the two pumps finish emptying the pond in half an hour.       Log On


   

Question 564144: A pond is being drained by a pump. After 3 hours, the pond is half empty. A second pump is put into operation, and together the two pumps finish emptying the pond in half an hour. How long would it take the second pump to drain the pond if it had to do the same job alone.
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Pump A -3 hours
so it does 1/3 of the job in 1 hour
Pump A + B = 1/2 hour
so they do 1/(1/2) of the job in 1 hour=2
difference = 2-1/3= 5/6 of the job in 1 hour
so for 1 job Pump B will take 6/5 hours
1 1/5 hours

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of pumping for the 1st pump
is +%281%2F2%29+%2F+3++=+1%2F6+ ponds/hr
Let the rate of the 2nd pump = +1%2Ft+ ponds/hr
-----------
Working together,
++1%2F6+%2B+1%2Ft+=+1%2F%28%281%2F2%29%29+
+1%2F6+%2B+1%2Ft+=+2%2F1+
Multiply both sides by +6t+
+t+%2B+6+=+12t+
+11t+=+6+
+t+=+6%2F11+ hrs
The 2nd pump can drain 1 pond in 6/11 hrs
This is 32.727 min
32 min and 44 sec