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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 significance@rss.org.uk. Explain how you came up with the solution, as we may publish a selection of correct entries (if received by 9 May 2022).