Answer:
It takes 36 minutes to fill the bathtub using just hot water.
Explanation:
We are gonna name V the complete volume of the bathtub, which is filled a certain amount of minutes. Each filling rate or speed is gonna be expressed as:
.
So, if we apply this consideration to each case we have:
Using cold and hot water:

Using only cold water:

Using only hot water:
; because we don't knot the time it takes to fill the bathtub with hot water.
Now, as you can see, Cold and Hot water is a sum of cold water only and hot water only:

Solving the equation for x:

Therefore, it takes 36 minutes to fill the bathtub using just hot water.