A tyre has two punctures. The first puncture alone would have made the tyre flat in 6 minutes and the second alone would have done it in 9 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(3\frac{3}{5}\) minutes
This works like two pipes emptying a tank: a puncture that empties the tyre in \(n\) minutes lets out \(\frac{1}{n}\) of the air each minute, and when both leak together their rates add.
Air let out per minute by both \(\displaystyle =\frac{1}{6}+\frac{1}{9}=\frac{3+2}{18}=\frac{5}{18}\)
Time to go flat \(\displaystyle =\frac{18}{5}=3\frac{3}{5}\) minutes