Question 31642
Hello!
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If the tub can be filled in 6 minutes with the faucet turned on, then the faucet fills 1/6 of the tub per minute.

Similarly, if a full tub can be emptied in 11 minutes when the drain is open, then the drain "fills" -1/11 of the tub per minute (filling a negative amount would be equivalent to draining it)

Therefore, when they are both working, they can fill:

{{{1/6 + (-1/11) = 1/6 - 1/11 = (11-6)/66 = 5/66}}} of the tub per minute.

Based on this, we condlude that it will take 66/5 = 13.2 minutes to fill an empty tub when the faucet is turned on and the drain is open.


I hope this helps!
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