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
![(1)/(18)+ (1)/(H) = (1)/(12)](https://img.qammunity.org/2019/formulas/mathematics/high-school/69kx9r6cfcnltkjn8us8dnotytbcbqc1zi.png)
. We need a common denominator, which is 36.
![(2)/(36) + (1)/(H) = (3)/(36)](https://img.qammunity.org/2019/formulas/mathematics/high-school/4vtlaoi0vi87v0fne0o0qjwli9hk8jwo12.png)
. Doing the simplifying we have
![(1)/(H)= (1)/(36)](https://img.qammunity.org/2019/formulas/mathematics/high-school/yjo2cb6slqdea6ennijerfbznnv5di1vx9.png)
and H = 36 minutes.