SOLUTION: A water faucet can fill a sink in 6 minutes, whereas the drain can empty it in 4 minutes. If the sink is full, how long will it take to empty if both the faucet and drain are both

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A water faucet can fill a sink in 6 minutes, whereas the drain can empty it in 4 minutes. If the sink is full, how long will it take to empty if both the faucet and drain are both       Log On


   

Question 528086: A water faucet can fill a sink in 6 minutes, whereas the drain can empty it in 4 minutes. If the sink is full, how long will it take to empty if both the faucet and drain are both open?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A water faucet can fill a sink in 6 minutes, whereas the drain can empty it in 4 minutes. If the sink is full, how long will it take to empty if both the faucet and drain are both open?
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1/6=flow-rate of faucet
1/4=flow-rate of drain
x=minutes to empty sink when faucet and drain are both open
1/x=net flow rate when faucet and drain are both open
..
1/4-1/6=1/x
3/12-2/12=1/x
1/12=1/x
x=12 minutes
ans:
It would take 12 minutes to empty sink when faucet and drain are both open
Check:
The faucet would add water for 2 full sinks=1/6*12=2
The drain would take out water for 3 full sinks=1/4*12=3 (existing full sink plus 2 added by faucet)