A sink can be filled by a pipe in 6 minutes but it takes 12 minutes to drain a full sink. If both the pipe and the drain are open, how long will it take to fill the sink?

Answer 1

ratedraining= 1sinkluff/12min
ratefilling=1sinkfull/6min

time= 1 sink/(1/12+1/6)=12*6/(6+12)=4 min

Answer 2

seems to me like the sink is being filled at the rate of 1/6 - 1/12 = 1/12 sink/min, so it will take 12 minutes to fill it if the drain is open.