# Maths for fun on run

Doing simple maths is one of my favourite things to do on solo runs1. I try to calculate my pace based on distance and time on the watch2, or I try to calculate the time it’d take me to the finish, or most commonly, I calculate the pace I need to run to finish a race in under a certain time.

Today’s schedule had an easy 55 min run, so distance and pace weren’t very relevant. I was instead thinking whether I’ll complete 15000 steps by the time I got home.

I had about 4500 steps after the boys’ walk. I walked around the house a bit—changing, procrastinating, feeding the boy, warming up, etc. So, I could assume I would have had ~5000 steps when I started the run. Here’s a simplified version of how the calculation went:

My metronome was set at 182 beats per minute, so I could assume I’d have an average cadence of at least 182 steps per minute. Total steps would thus be…

= 182 * 55
= (180 + 2) * 55
= 180 * 55 + 2 * 55
= 180 * 55 + 110
= 180 * (1.1 * 50) + 110
= (180 * 1.1) * 50 + 110
= 198 * 50 + 110
= 198 * (100 / 2) + 110
= (198 / 2) * 100 + 110
= 99 * 100 + 110
= 9900 + 110
= 10010 steps

That should get me past the 15K mark :)

Later, on the way back up the hill, the watch buzzed to tell me I’d completed 10000 steps (for the day). I’d run ~27 mins at that point. It was the cue for the next mental maths for fun. Here’s how it went (again, grossly simplified):

Starting with total run time of 55 mins, steps I expected to get in the remainder of the run were:

= (55 – 27) * 182
= 28 * 182
= 28 * (180 + 2)
= 28 * 180 + 28 * 2
= 28 * 180 + 56
= (30 – 2) * 180 +56
= 30 * 180 – 2 * 180 +56
= 30 * 180 – 360 + 56
= 30 * 180 – 304
= 3 * 18 * 100 – 304
= 54 * 100 – 304
= 5400 – 304
= 5096 steps

Still on track to make it to 15000 steps.

Here’s what the watch said when I got home :) Yes, I went for a run. After I poured out my sorrow in the last post, I got up, got dressed, and went for the run.

It was a good run. My form was good, and HR was low and steady, even on the return uphill in the sun. I’m still not feeling great, but am in a much better state than before the run. I was a 2 when I wrote that post, 8 on the run, and probably a 6 now. (Don’t all the turnaround days have a good run or swim in them?)

1. Doing the math specially helps when there are thoughts I’m trying to keep out of the head. Like today.
2. I’ve set up my watch screen to not show running pace. This keeps my mind on how I’m running, rather than on how fast I’m running. It also gives me something to do with my head—calculate that pace :) . The four fields on the main screen are distance, duration, current HR zone, and mean cadence.

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