Select the correct answer. A faucet can fill a bathtub in 6 minutes. The drain can empty- the tub in 10 minutes. If both the fauc is represented by this expression, where \( t \) is the number of minutes it will take to completely fill the \( \frac{t}{6}-\frac{t}{10} \) Which expression can also represent this situation? A. \( \frac{4 t}{15} \) B. \( \frac{t+16}{60} \) C. \( \frac{t^{2}}{60} \) D. \( \frac{t}{15} \)

To determine the correct expression that represents the situation where a faucet fills a bathtub while a drain empties it, let's analyze the problem step by step. ### Given: - **Faucet's filling rate:** The faucet can fill the bathtub in 6 minutes. This means the faucet fills \( \frac{1}{6} \) of the tub per minute. - **Drain's emptying rate:** The drain can empty the bathtub in 10 minutes. This means the drain empties \( \frac{1}{10} \) of the tub per minute. ### Net Rate of Filling: When both the faucet and the drain are open simultaneously, the net rate at which the tub is being filled is the filling rate minus the emptying rate: \[ \text{Net rate} = \frac{1}{6} - \frac{1}{10} \] To subtract these fractions, find a common denominator (which is 30): \[ \frac{1}{6} = \frac{5}{30}, \quad \frac{1}{10} = \frac{3}{30} \] \[ \text{Net rate} = \frac{5}{30} - \frac{3}{30} = \frac{2}{30} = \frac{1}{15} \] This means the tub is being filled at a rate of \( \frac{1}{15} \) of the tub per minute when both the faucet and the drain are open. ### Expression Representation: Given that \( t \) is the number of minutes it takes to completely fill the tub, the total amount filled can be represented by: \[ \frac{t}{6} - \frac{t}{10} = \frac{t}{15} \] This simplifies to: \[ \frac{t}{15} \] ### Conclusion: Among the provided options, the expression \( \frac{t}{15} \) accurately represents the situation. **Answer:** **D. \( \frac{t}{15} \)**