A tyre has 2 punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?

Let assume that flattening a tyre is equivalent to work of 18 units (which is LCM of 9,6)

Time taken by 1st puncture to made a tyre flat = 9 minutes

In 1 minute,1st puncture releases = 2 units of air

Time taken by 2nd puncture to made a tyre flat = 6 minutes

In 1 minute,2nd puncture releases = 3 units of air

If both punctures happen together then in 1 minute amount of air released from tyre = 2 + 3 = 5 units

then time taken by both tyres to release the air = $$\frac{18}{5}$$ = 3 $$\frac{3}{5}$$ minutes