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?
Since the ratio of flat distance and hill distance is not given, at first glance it looks like not enough information is given. If the problem is solvable, this suggests the answer does not depend on the relative amounts of level running and hill running. If so, we can assume the hill running distance is zero and the entire 2 hour run is at 6 mph.
So the distance between the house and point of return is 6 miles.
But let's check and make sure.
The total distance D is the sum of the flat distance x plus the hill distance h.
Dividing the run into 4 time increments:
x/6 + h/4.8 + h/8 + x/6 = 2 hours
x/3 + h/4.8 + h/8 = 2 hours
combine: h/4.8 + h/8 = (8+4.8)h / (4.8*8) = (12.8/38.4)*h = h/3
x/3 + h/3 = (x+h)/3 = 2 hours
D= x+h = (3 miles/hour) * (2 hours) = 6 miles
This apparent coincidence occurs because the harmonic mean of 4.8 and 8 happens to be 6
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Posted by Larry
on 2021-02-24 17:42:18 |
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