Question

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 faucet and the drain are open at the same time, this situation is represented by this expression, where \\(t\\) is the number of minutes it will take to completely fill the bathtub.

\\\frac{t}{6} - \frac{t}{10}\\

which expression can also represent this situation?

\\(\bigcirc \frac{t + 10}{60}\\)
\\(\bigcirc \frac{t}{60}\\)
\\(\bigcirc \frac{t}{15}\\)
\\(\bigcirc \frac{4t}{15}\\)

Explanation:

Write the given expression

$$ \frac{t}{6} - \frac{t}{10} $$

Find a common denominator

$$ \text{LCM}(6, 10) = 30 $$

$$ \frac{t}{6} - \frac{t}{10} = \frac{5t}{30} - \frac{3t}{30} $$

Simplify the expression

$$ \frac{5t - 3t}{30} = \frac{2t}{30} = \frac{t}{15} $$

Answer:

• (A) \(\frac{t + 10}{60}\)
• (B) \(\frac{2t}{60}\)
• (C) \(\frac{t}{15}\) (Correct answer)
• (D) \(\frac{4t}{15}\)