Speed and Stop Time Calculation from Google Maps Data

Problem

Solution

Let the 2 known points be A and B. To solve for a and b for point A:

Substitution of b into original eqn for point B:

To find b, substitute a back into the equation for b

Checking

Using the following input as sample:

{stops=32, distance=39.081000 km, time=66.000000 min}
{stops=31, distance=36.573000 km, time=62.000000 min}

Answer should be:

a = speed = 0.66411...
b = stopTime = 0.2235337...

Error Handling

If any of the 2 data points return "null", only one data point can be used. To handle this, the stopTime (b) is assumed to be a default value.

Coding

Final Equations

Optimization

To optimize calculations, number of divisions should be decreased. This is because based on Intel's arithmetic latencies. The following equations and corresponding pseudocode is proposed.

In the pseudocode, speed refers to the mathematical constant a while stopTime refers to the constant b. a and b refer to the 2 data points.

sRatio = b.stops / a.stops
speed = (b.distance - sRatio*a.distance)/(b.time - sRatio*a.time)
stopTime = (a.time*speed - a.distance)/(a.stops * speed)