## A Travel Puzzle

The following cute puzzle of unknown origins was sent to me by Martina Balagovic and Vincent van der Noort:

A car travels from A to B and back again. When going uphill it goes 56 km an hour, when going downhill it goes 72 km an hour and while driving on flat surface it goes 63 km an hour. Getting from A to B takes 4 hours and getting back (over the same road) takes 4 hours and 40 minutes.
What is the distance between A and B?

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1. #### Leo:

That’s a cute puzzle! What’s the intended age of its target audience?

2. #### Sam Hardwick:

Lewis Carroll had a similar problem in his A Tangled Tale. Here’s a tweet with a picture from the summary and answer section: https://twitter.com/SKRHardwick/status/729329381429157888

3. #### Vincent:

Sam Hardwick: thank you! I always wondered who created this puzzle, and it is a really nice surprise to see that it is this old!

4. #### tanyakh:

Leo, as usual the target audience if from 8 to infinity.

5. #### Marcial Fonseca:

Hi there,
Without algebra, just v=e/t, 273 km

6. #### Christian Lawson-Perfect:

I’m fairly certain I first saw this as a Car Talk Puzzler, but I can’t find it in their archives. Hardly Lewis Carroll, but I’d love to find the Car Talk reference again – there was some great discussion by the hosts.

7. #### Jeremy:

I love the elegance of the solution; the combined trip from A to B back to A eliminates any algebra.