Discussion
A tap can fill a tank in 48 minutes where as another tap can empty it in 2 hours. If both taps are opened at 11.40 AM, then the tank will be filled at .. ?
Answer: B
Put both rates over a common unit of minutes. The filling tap does \( \tfrac{1}{48} \) of the tank each minute and the emptying tap removes \( \tfrac{1}{120} \), since 2 hours is 120 minutes:
\[ \frac{1}{48} - \frac{1}{120} = \frac{5 - 2}{240} = \frac{3}{240} = \frac{1}{80} \]
So the tank fills in 80 minutes, that is 1 hour 20 minutes.
\[ 11{:}40\text{ AM} + 1\text{ h }20\text{ min} = 1{:}00\text{ PM} \]
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