Let's see... By the data of the problem, I suppose the pipes supply water at a constant rate. For the first pipe, call this rate . If the pipe supplies units of water in time t minutes, then we have
, which integrates to the term being the initial supply at time . I guess , as we have to set the timer and open the tap simultaneously ( ). If the tub fills at units of water, then , and so . We conclude that, for the first pipe, the supply is .
Under the same suicidal considerations, we obtain that the supply of the second pipe is . For both pipes, the supply is (almost). When the tub fills, we will have , from where minutes...
The tub is full. Now, lets give president Bush a bath.