On my jogging days I start at 6:00 sharp and follow a paved road, heading strictly North.
At some point this same-level road turns West, but I go on on a path heading North going uphill till I reach an antenna site located on top of the hill.
I rest there for 10 minutes exactly then return following the same route in opposite direction.
I arrive home at 08:10.
My average speeds are: on the paved road 6 mph, uphill 4.8 and downhill 8,
What is the distance between my home and the point of return?
Done in my head in about 5 seconds. If there is a solution, it must be 6 miles.
The problem does not indicate the relative amount of time spent on the flat vs. on the hill, so it must be irrelevant. Assume that the hill is an anthill, and that all the time is spent running on the flat. Then I spend one hour going and one hour returning, at 6 mph, so the distance must be six miles.
(Note, in order for this problem to be solvable, it must be the case that 4.8 uphill and 8 mph downhill averages out to 6 mph. That would be easy to check, but this is a timed competition and I am already on to the next problem.)
Mathlete solution (spoiler)
