A tyre has 3 punctures. The first puncture alone would have made the tyre flat in 9 minutes, the second alone would have done it in 18 minutes, the third alone would have dore it in 6 minutes. If the air leaks out at a constant rate, then how long (in minutes) does it take for all the punctures together to make it flat?

3

According to question ,

The first puncture alone would have made the tyre flat in 9 minutes

So , In 1 minute, the first puncture can make \(\frac{1}{9}\)th of the tyre 

The second puncture alone would have made the tyre flat in 18 minutes

So , the second puncture can make \(\frac{1}{18}\)th of the tyre flat In 1 minute

The third puncture alone would have made the tyre flat in 6 minutes

So , In 1 minute, the third puncture can make \(\frac{1}{6}\)th of the tyre flat 

In 1 minute, the all tyres can make \(\frac{1}{9}\) + \(\frac{1}{18}\) + \(\frac{1}{6}\) = \(\frac{1}{3}\) of the tyre flat

Total required time to flat = 3 minutes

Hence , All punctures can make the tyre flat in 3 minutes