# Puzzle: Oh no! Puncture!

Driving in France recently, I got a puncture in my tyre. I was 13 km from my hotel and needed to get back, but for each kilometre I drove my tyre got flatter, so I had to drive more slowly.

For the first kilometre I drove at a constant speed. For the second kilometre I drove at a slower constant speed. Similarly, for each of the remaining kilometres I drove at constant (albeit decreasing) speeds. My average speed for the first 2 km was a whole number of kilometres per hour, as were my average speeds for the first 3 km, 4 km, 5 km, …. Indeed, the average speeds for the first i km of my journey back to the hotel were whole numbers of kilometres per hour, all the way up to i = 13.

The speed limit on the route was 100 km/h. How many minutes did it take me to drive the last kilometre back to my hotel? Send your answers to This email address is being protected from spambots. You need JavaScript enabled to view it.. Explain how you came up with the solution, as we may publish a selection of correct entries (if received by 9 May 2022).