Question

It takes 12 minutes to fill an entire bathtub using both the cold and hot water. If just the cold water is used, it takes 18 minutes to fill the bathtub. How long would it take to fill the bathtub if just the hot water were used?

Answer 1

If it takes 12 minutes to fill the tub using H and C, you can get 1/12 of the tub filled in 1 minute.  If you use just C it takes 18 minutes to fill it, and you can get 1/18 of the tub filled in 1 minute.  If you are looking to see how long it will take to fill the tub with just H, you can get 1/H of the tub filled in 1 minute.  H is our unknown.  Adding them together takes 12 minutes, so the equation we have is $\frac{1}{18}+ \frac{1}{H} = \frac{1}{12}$.  We need a common denominator, which is 36.  $\frac{2}{36} + \frac{1}{H} = \frac{3}{36}$.  Doing the simplifying we have $\frac{1}{H}= \frac{1}{36}$ and H = 36 minutes.