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?
(In reply to
Puzzle Answer by K Sengupta)
Let the paved road distance be p miles, and:
The hill road distance be h miles, and:
The total distance traversed be T miles.
By the problem, the total time taken (not including the 10 minutes rest) is:
8:10 - 6:00 - 10 min. = 2 hrs.
Thus, we must have:
(h/4.8 +p/6) + (p/6 +h/8) = 2
Now, h/4.8 + p/6+p/6+h/8
= p/3+(h/4.8+h/8) = p/3+(5h+3h)/24
= p/3+8h/24 = (p+h)/3
Accordingly, we must have:
(p+h)/3 = 2
=> p+h = 6
Now, we observe that T = p+h = 6
Consequently, the required distance between the individual's home and his point of return must be 6 miles.
Explanation to Puzzle Answer
