Solution:
Given that,
A cold water faucet can fill the bathtub in 12 minutes
A hot water faucet can fill the bathtub in 18 minutes
The drain can empty the bathtub in 24 minutes
Let "t" be the time taken to fill the bath tub
Both faucets are on and the drain is open, therefore, in one minute, they can fill,
[tex]\frac{t}{12} + \frac{t}{18} - \frac{t}{24} = 1[/tex]
Here, negative sign means "drain can empty"
[tex]t( \frac{1}{12} + \frac{1}{18} - \frac{1}{24} ) = 1 \\\\t( \frac{1 \times 6}{12 \times 6} + \frac{1 \times 4}{18 \times 4} - \frac{1 \times 3}{24 \times 3 }) = 1\\\\t( \frac{6}{72} + \frac{4}{72} - \frac{3}{72}) = 1\\\\t \times \frac{7}{72} = 1\\\\Therefore,\\\\t = \frac{72}{7}\\\\t = 10.285 \approx 10.3[/tex]
Thus, it takes 10.3 minutes to fill the bath tub
