The function *tfinal* that I developed for part 3 returns the time for the two friends to complete a journey as a function of six variables: the total distance (*s*), the distance ahead of the other friend that the rider leaves the bicycle (*h*), and the walking and riding speeds of each friend (*wA,rA,wB, *and* rB *respectively). The graph of completion time vs. distance ahead is so strange-looking that I decided I wanted to see what the whole process looked like for given values of *wA, rA, wB, rB, s,* and *h*. That meant writing a function to return a data frame containing the elapsed time and the position of each friend and the bicycle at the end of each event.

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# Sharing a bicycle (part 3)

Having derived the equations of motion, it’s a simple matter to translate the math into R code. As we’ll see, the difficult part is understanding the results. The code is below; the most important part is the function *tfinal*, which implements the four steps as described in previous posts. There are a lot of if statements, and if it weren’t for the *return* statement I’m not sure how I would have worked this out. This is one case where I really felt the need for a goto statement.