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. \( \frac{t}{15} \)
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Let's calculate the relationship between the faucet filling the bathtub and the drain emptying it. The faucet fills the tub at a rate of \( \frac{1}{6} \) of the tub per minute, while the drain empties it at a rate of \( \frac{1}{10} \) of the tub per minute. When we combine these rates, we can represent the net filling rate as: \[ \text{Net Rate} = \frac{1}{6} - \frac{1}{10} \] Finding a common denominator (which is 30) gives: \[ \frac{5}{30} - \frac{3}{30} = \frac{2}{30} = \frac{1}{15} \] Thus, the entire expression for the situation is \( \frac{t}{15} \) (since it denotes how much of the tub is filled over time \( t \)). Therefore, option D \( \frac{t}{15} \) is the correct answer. Now, let's have some fun with this! If you ever wondered how much math is involved in your everyday life, think about your bathtub! Balancing the rates of filling and draining involves a bit of algebra, but it’s a practical illustration of using fractions, a skill you employ in countless scenarios, from cooking to budgeting! Also, have you ever considered how your choice of faucet affects water usage? Choosing one with better flow efficiency can significantly reduce your water bill and conserve resources. It’s not just about filling the tub; it’s about ensuring we're bathing sustainably!
