Ttakes 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?

V is a volume of the water that can be in the bathtub.
Rate of filling of the bathtub with water = Volume/time.

Rate of filling with cold water = V/18.

x min is the time filling with the hot water.
Rate of filling with hot water = V/x.

Rate of filling with cold and hot water = V/12.
At the same time, rate of filling with cold  and hot water = V/18 + V/x.

V/18 + V/x = V/12

1/18 + 1/x = 1/12
1/x = 1/12 - 1/18
1/x = 3/36 - 2/36
1/x = 1/36
x = 36 min