It takes four minutes to fill a bathtub if the hot and cold water taps are both on and the stopper is in. It takes six minutes to empty the tub if the taps are off and the stopper is out. How long does it take to fill the tub if both taps are on and the stopper is out?

Answer:12 minutesStep-by-step explanation:Since it takes 4 minutes to fill the bathtub with both taps on and stopper is in then for each minute the 2 taps can fill up to a quarter (1/4) of the tub:Similarly, it takes 6 minutes to drain the tub with both taps off and the stopper is out. This means for each minute the stopper can drain one sixth (1/6) of the tub.Therefore, when both taps are on and the stopper is out, then for each minutes, the amount of water remaining in the tub is the water flowing in minus the water draining out[tex]\frac{1}{4} - \frac{1}{6} = \frac{3}{12} - \frac{2}{12} = \frac{1}{12}tub[/tex]So for each minute, one twelveth of the tub is filled, for the tub to be completely filled in, it would take 12 minutes