Treadmill Distance Math

While walking on the treadmill today – a great place/time to think, by the way – I started calculating exactly how long it would take, at a fixed-pace, to walk a mile.

My particular treadmill does this calculation for me, but with nothing to do but walk, I figured I’d work out the math anyway.

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We measure speed in miles per hour.  There are 60 minutes in one hour.  Here’s the basic equation for figuring out how long it takes to walk 1 mile, given a fixed speed.

60 minutes / x (minutes to walk 1 mile) = speed (in mph) / 1

Using 3.7 mph, let’s figure out how long it takes to walk one mile.

60  min / x = 3.7 mph  / 1

A little old-school cross-multiplication yields

60 = 3.7x

x = 60/3.7

x = 16.22 minutes

We then need to convert the .22 minutes to seconds

60 seconds per minute * .22 minutes = 13 seconds

So, it takes 16 minutes 13 seconds to walk 1 mile at 3.7 mph.

Here is a quick chart with speeds from 2 mph to 6.5 mph.

Speed            Time (m/s)

2.0      0:30:00
2.1      0:28:34
2.2      0:27:16
2.3      0:26:05
2.4      0:25:00
2.5      0:24:00
2.6      0:23:04
2.7      0:22:13
2.8      0:21:25
2.9      0:20:41
3.0      0:20:00
3.1      0:19:21
3.2      0:18:45
3.3      0:18:10
3.4      0:17:38
3.5      0:17:08
3.6      0:16:40
3.7      0:16:13
3.8      0:15:46
3.9      0:15:23
4.0      0:15:00
4.1      0:14:38
4.2      0:14:17
4.3      0:13:57
4.4      0:13:38
4.5      0:13:19
4.6      0:13:02
4.7      0:12:45
4.8      0:12:30
4.9      0:12:14
5.0      0:12:00
5.1      0:11:45
5.2      0:11:32
5.3      0:11:19
5.4      0:11:06
5.5      0:10:55
5.6      0:10:42
5.7      0:10:31
5.8      0:10:20
5.9      0:10:10
6.0      0:10:00
6.1      0:09:50
6.2      0:09:40
6.3      0:09:31
6.4      0:09:21
6.5      0:09:13

Most treadmills will do these calculations for you, but it’s cool to re-visit some per-algebra once in a while.  I rounded when making calculations, so I could be off by a second-or-two.  Let me know if you find an error in my calculations.  Be blessed.

I used some of the great information found at Fitness Math to verify my calculations.

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