# Plep's Puzzles

Name:

## Saturday, October 09, 2004

### Two Travellers

Two walkers spend from 3 pm until 9 pm walking along a level road, walking up a hill, and reversing their steps down the hill and back along the level road to return back home again. Their pace on the level is 4 mph, uphill 3mph, and downhill 6 mph.

How far did they walk?
To the nearest half hour, at what time did they reach the top of the hill?

The next puzzle will about a week from when this one was published!

Sean said...

Sorry I keep answering these before anyone gets a chance to - I look forward to them all week. Which might suggest it's time for me to get a hobby.

They walked a total of 24 miles, and they reached the top of the hill at 6:30.

No help from the girlfriend this time - which may prove to be a bad thing.

October 10, 2004 at 6:57 PM
steven said...

That's it.

To travel and return one mile on the level takes 1/4 + 1/4 = 1/2 an hour. To travel and return one mile uphill then downhill takes 1/3 + 1/6 = 1/2 an hour. So to travel and return over a mile must take the same time, whether the mile is level or hilly. In 6 hours the walkers went 12 miles out + 12 miles back = 24 miles.

If the route was almost all level (say the hill is a molehill!), the walkers would have walked the 12 miles out in 12/4 = 3 hours, so they would have arrived at the top of the 'hill' at 6 pm.
If the route was almost all hilly, they would have walked the 12 miles out in 12/3 = 4 hours, arriving at the top of the hill at 7pm.
Therefore, the walkers arrived at the top of the hill within 1/2 an hour of 6:30 pm.

This puzzle is from Lewis Carroll's 'A Tangled Tale', which was published in installments for 'The Monthly Packet' in 1880. I'll put one of my own in sooner or later, promise!

(BTW, no worries about doing the puzzle first - those who have a need to solve it for themselves can always do it and read the comments later ;) ).

October 11, 2004 at 12:29 PM