One pipe can fill a tank five times as fast as another pipe. If, together, two pipes can fill the tank in 30 minutes, how much time does the faster pipe alone take to fill the tank?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 36 minutes
Let the slower pipe fill the tank in t minutes. The faster pipe is five times as fast, so it takes \( \frac{t}{5} \) minutes.
Together they fill \( \frac{1}{30} \) of the tank per minute, so the work done per minute adds up:
\( \displaystyle \frac{1}{t}+\frac{5}{t}=\frac{1}{30} \)
\( \displaystyle \frac{6}{t}=\frac{1}{30} \)
\( \displaystyle t=180 \)
\( \displaystyle \text{faster pipe}=\frac{180}{5}=36\ \text{minutes} \)