The main reason you can only do 40mph on the way down is because of air (and a bunch of other real-world limitations). In a vacuum, what would your average speed be at the end of a 5 mile 10% descent assuming you just coasted and your bike would not blow up when you hit 100mph?

I guess this might still be compounding the problem because your are further shortening you descending time, but air resistance is a key inhibitor that keeps us from beeing able to take full advantage of gravity (we feel it's full effects on the way up, but see limited benefits on the way down).

With a computer taking speed data for average speed, wouldn't it take more units on the uphill because it takes longer?

Golly you guys are smart.

It does indeed. The heavier cyclist's ratio of weight-to-surface area is more advantageous. Even though the two cyclists might weigh stones apart, their surface area will [usually] vary by a much smaller amount.

A problem that clearly illustrates this is a car traveling 1 mile @ 60mph. How fast does it need to go on the 2nd mile to average 120mph? Hint: it isn't 240mph.


Answer: impossible / infinite mph. 2 miles @ 120mph = 1 minute. You've already taken the full minute traversing your 1st mile.

and theres a machine involved - the wheel - the heavier person exerts more force on the machine and produces more work; i.e.: speed

Downhill

F = m * g (For all you non physicist, Force equals Mass * gravity)

Since gravity stays @ 9,8 m/s Squared. A person with more mass will have a greater downward force.

but if a fat guy and a skinny guy jumped off a roof wouldn't they both hit the ground at the same time?

Theoretically no, though it might be close (have no idea exactly how close it would be). The extra mass of the fat guy lets him oppose the air resistance a little better than the skinny guy. If air weren't a factor, they would both hit the ground at the same time.

Edit: Now that I think about it, maybe the skinner guy is more aero since he has less of a profile. So maybe the skinny guy will hit first. Anyway, the point is that air resistance complicates things, but it's not the reason why the average mph in the problem in the OP isn't simply the average of the uphill speed and the downhill speed.

This depends, why do they jump?

Yeah, the point of the assignment wasn't to explore the affects of power, wind resistance, etc. on how fast you can go. It was to point out what I had thought was obvious: Its not the distance at a speed that influences MPH, its the time. After all, the H in MPH stands for "Hour". If we were discussing PPM (pace per mile), it would be different.

The M in MPH stands for Miles, so distance is a pretty important part of the calculation also.... I'm not sure what pace per mile would mean, but it MPH is a pace I think.

But its miles PER hour.

I may not be using the terms correctly, but to me, pace is time per distance-- minutes per mile. In my original example, 10 mph is 6 minutes per mile, and 30 mph is 2 minutes per mile. the average pace for the 2 miles would be 4 minutes per mile. I think.