One pump can fill a reservoir in 60 hours. Another pump can fill the same reservoir in 80 hours. a third can empty the reservoir in 90 hours. If all three pumps are operating at the same time, how long will it take to fill the reservoir?

1/time needed = 1/time of 1st pump + 1/time of 2nd pump - 1/time of 3rd pump

1/t = 1/t1 + 1/t2 - 1/t3

1/t = 1/60 + 1/80 - 1/90

1/t = 12/720 + 9/720 - 8/720

1/t = 13/720

t = 720/13 hours = 55.38 hours = 55 hours 23 minutes

536

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