Final answer:
By subtracting the rate of filling the bathtub with cold water from the combined rate of hot and cold water, we find that it would take 36 minutes to fill the bathtub using just the hot water. The correct answer is B) 36 minutes.
Step-by-step explanation:
The question involves solving a rate problem using simple algebra. The rates at which the hot and cold water fill the bathtub are additive when both are used simultaneously. If the cold water takes 18 minutes to fill the bathtub, its rate of filling is 1/18 bathtubs per minute. When both hot and cold water are used, the combined rate is 1/12 bathtubs per minute. To find the rate of the hot water alone, we can subtract the cold water's filling rate from the combined rate. Let's denote the hot water's filling rate as 1/h, where h is the time in minutes to fill the bathtub using just the hot water.
When combined, the equation is:
1/18 + 1/h = 1/12
By solving this equation for h, we can find the time it takes for the hot water to fill the bathtub:
1/h = 1/12 - 1/18
1/h = 3/36 - 2/36
1/h = 1/36
So, h = 36 minutes to fill the bathtub using just the hot water.
Therefore, the correct answer is B) 36 minutes.