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 email@example.com. Explain how you came up with the solution, as we may publish a selection of correct entries (if received by 9 May 2022).
- Puzzle set by Michael Fletcher and published in the April 2022 issue of Significance.
- Try your hand at Michael’s previous puzzle, “How many balls in the bag?“, and read the solution in our latest issue (magazine subscription required).