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mathalgebra

Solve for variable, to calculate GAP from speed and grade

(speed * 0.2) + 3.5 = ((gap * 0.2) + 3.5) + (gap * grade * 1.8)

Trying to rearrange this to solve for GAP, given that speed and grade are known. My algebra is struggling. Anyone have any suggestions on how to rearrange this equation?

EDIT: Trying to rearrange to be used as formula for calculating GAP (grade adjusted pace) based on Speed and Grade while parsing GPS data.

Based on the below accepted solution: $gap = $speed / (1 + (9 * $grade))

Solution

  • (speed * 0.2) + 3.5 = ((gap * 0.2) + 3.5) + (gap * grade * 1.8)

    Subtract out the 3.5 from both sides.

    (speed * 0.2) = (gap * 0.2) + (gap * grade * 1.8)

    Multiply both sides by 5 (purely visual).

    speed = gap + (gap * grade * 9)

    Factor out gap on the RHS.

    speed = gap * (1 + (grade * 9))

    Divide both sides by the grade factor.

    gap = speed / (1 + (9 * grade))