SOLUTION: Tap A takes 6 minutes to fill a tank and Tap B takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. How long will it take to fill up the tank if the pipe
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-> SOLUTION: Tap A takes 6 minutes to fill a tank and Tap B takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. How long will it take to fill up the tank if the pipe
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Question 1117269: Tap A takes 6 minutes to fill a tank and Tap B takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. How long will it take to fill up the tank if the pipe is in use when both taps are turned on? Found 2 solutions by math_helper, ikleyn:Answer by math_helper(2461) (Show Source):
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The approach is to see how much of the tank fills in a unit of time. A good choice for the unit of time is one minute, because the fill and empty times are given in minutes. We of course assume the tank is empty at the start.
A fills 1/6 of the tank per minute.
B fills 1/9 of the tank per minute.
C "fills" -1/15 of the tank per minute. Here the minus sign indicates it is actually emptying the tank.
Fill rate = tanks per minute
The time needed to fill one tank is therefore or about minutes (4 min, 44.2 sec).
Check: This is more of a qualitative check. Does our answer make sense?
Say the pipe emptying the tank was turned off. The two taps would fill the tank at a rate (1/6)+(1/9) = 5/18 tank/min. This corresponds to a fill time of 18/5 = 3.6 minutes. In the problem scenario the pipe is emptying the tank at 1/15 tank/min which is comparatively slower than the fill rate, so we'd expect the fill time to be extended, but only moderately. Our answer of 4.7368 minutes is moderately longer than 3.6 minutes so at least the answer seems about right.
