Final answer:
After setting up and solving a proportion based on the given direct variation (4 inches/9 seconds = 15 inches/x seconds), the answer appears to be 33.75 seconds, which does not match any of the provided options. Therefore, there might have been an error in the problem's setup or options.
Step-by-step explanation:
The question involves a situation where the height of water in a bucket varies directly with the number of seconds that the faucet has been on. This means if you double the time, you'll double the height of the water, and so forth. We know that after 9 seconds, the water is 4 inches high. To solve for the time it would take for the water to be 15 inches high, we use the concept of direct variation.
First, we set up a proportion because the situation describes a direct variation:
4 inches / 9 seconds = 15 inches / x seconds
By cross-multiplying, we get:
4 * x = 9 * 15
So,
x = (9 * 15) / 4
x = 33.75 seconds
However, this does not match any of the options provided, which indicates there might have been a mistake in either the setup of the problem or in the provided options. Therefore, I cannot confidently select any of the answers (A, B, C, D) given in the question.