Wednesday, July 21, 2010

How much jog could a jogger jog...

My normal workout bike rides take about one hour to cover 25 km, going out along the Tamagawa river from Noborito to a landmark point near Fuchuu and then back. During this time, my mind will wander and I'll try to find something to keep it occupied. Math problems work, sometimes.

Quite often, I'll encounter this one specific jogger, and the question that came up was "how fast is he and how much ground is he covering between the two times I pass him?" Here's how it works.

As I'm riding along out along the river, I pass the jogger at 16 minutes into my ride. When I get to the turnaround point, I check the time - 28 minutes. I then meet him again at 35 minutes. When I get home, I check the clock one last time - 1 hour exactly. What was the jogger's speed?

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The answer's fairly straightforward, but the arithmetic is a bit hard to do in my head during the ride.

The route is 12.5 KM each way. If I ride out in 28 minutes then I'm averaging 26.79 km/h, and if I'm passing the jogger at the 16 minute mark, it means that I've covered 7.14 km. Then, the ride back takes 32 minutes (1 hour - 28 minutes) because of a head wind, giving me an average of 23.44 km/h. Meeting the jogger at 35 minutes means that I've traveled 7 minutes from the turnaround point to him, which is 2.62 km (or, 12.5 - 2.62 = 9.76 km from my start point).

So, in the time between meetings (35-16) = 19 minutes, he's gone 9.76- 7.14 km; that's 2.62 km. Or, 8.28 km/h (5.17 mph).

It's much easier to do this in an Excel spreadsheet...

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