One problem with the Garmin Edge 800 ‘bike nav’ is that unless you press the reset button between rides it assumes the activities are linked and makes them continuous. And so my 30 mile cycle ride this weekend was automatically joined to my midweek 20 minute resting heart rate test.

This presented me with a problem when trying to calculate my average heart rate from the ride. A problem requiring an algebraic formula! Knowing the mathematical inclinations of my readership I thought I would present my formula for comment.

Total Heart Rate, HRt = 143 bpm

Total Time, T = 2 hours & 17 mins = 137 mins

Midweek Resting Heart Rate, HRr = 65 bpm

Midweek Resting Time, Tr = 20 mins

And now a brief interlude to allow you to produce your own formula(e) to calculate my ride average heart rate, X.

My initial (incorrect) attempt was: (Tr x HRr) + ((T-Tr) x X) = HRt

This didn’t compute so I realised I had forgotten to divide the left hand side by the total time, T to give the average.

My second attempt was thus:

Fairly straightforward I suppose, but good to get the maths brain working again.

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Aha – students who take Chemistry have been training me to use units conversion, so I took both sets of beats/min and multiplied by min to get # beats for resting and total. Then take ratio of (beats on ride)/(time for ride). It’s what your final formula shows. What I really like is the sum from bike to infinity of maybe the dot product of penny farthing and bike??!!!!! Reminds me of this cartoon:

http://zerooutoffive.blogspot.com/2009/12/dog-acorn-house-differential-equation.html

Bye bye for now … happy tree-housing!

Haha. I think the formula is used to calculate next year’s “state of the art” development in bike design. Possibly a curved frame or less spokes on the wheel. The permutations appear to be infinitesimal!