Final answer:
The sink will take 110 minutes to empty while both the faucet and drain are open, using the combined rate of the two. The drain empties faster than the faucet fills, resulting in a net emptying rate calculated by the difference of their inverse rates.
Step-by-step explanation:
The question involves calculating the time it takes to empty a sink with both the faucet and drain open, considering the rates at which they can fill and empty the sink, respectively. The faucet fills the sink in 11 minutes, and the drain empties it in 10 minutes. To solve this, we use the concept of rates adding together.
When the faucet is filling the sink, its rate is 1 sink per 11 minutes, or 1/11 sink/minute. For the drain emptying the sink, its rate is 1 sink per 10 minutes, or 1/10 sink/minute. Since the drain's emptying rate is faster than the faucet's filling rate, the overall rate is the difference of these rates, which is (1/10 - 1/11) sink/minute. To find a common denominator, we get (11 - 10) / (10 * 11) = 1/110 sink/minute.
To find how long it will take to empty one full sink, we calculate the reciprocal of the overall rate, which gives us 110 minutes to empty the full sink.