SOLUTION: the hot water faucet can fill a bathtub in 9 min and the cold water faucet can fill the bathtub in 12 min. the drain can empty the bathtub in 18 min. if the bathtub is empty, how l
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-> SOLUTION: the hot water faucet can fill a bathtub in 9 min and the cold water faucet can fill the bathtub in 12 min. the drain can empty the bathtub in 18 min. if the bathtub is empty, how l
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Question 1117460: the hot water faucet can fill a bathtub in 9 min and the cold water faucet can fill the bathtub in 12 min. the drain can empty the bathtub in 18 min. if the bathtub is empty, how long will it take to fill the bathtub if both hot and cold faucets are on and the drain is open??? Found 2 solutions by ikleyn, solver91311:Answer by ikleyn(52832) (Show Source):
The hot water faucet fills of the bathtub volume per minute.
The cold water faucet fills of the bathtub volume per minute.
The drain takes out of the bathtub volume per minute.
The net inflow rate is = = of the bathtub volume per minute.
Hence, it will take minutes = minutes = 7 minutes and 12 seconds to fill the bathtub
if both hot and cold faucets are on and the drain is open.
Solved.
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It is a typical and standard joint work problem.
If the hot water tap can fill the bathtub in 9 minutes, then the hot water tap must fill of the bathtub in one minute. Likewise, the cold tap fills of the tub in one minute and the drain empties of the tub in one minute. So altogether:
of the tub gets filled (because this is clearly a positive number) every minute, and it will take the reciprocal of the above sum in minutes to fill the tub, so since the lowest common denominator is 36:
It will take minutes or 7 minutes and 12 seconds to fill the tub if both taps and the drain are open.
John
My calculator said it, I believe it, that settles it
