The tendency to invert the presentation of a solution is well illustrated here. The fact that the result is independent of the track radius is found by solving the problem. Yet it is the first matter expressed above. Though the difference in circumferences is wanted, the presentation does not say so till after the things needed to compute the difference have been assembled. This assumes that the reader knows where the writer is headed.

The solution below removes this inversion by stating what is going to be done before it is done. The first equation states that the difference in circumferences is needed. This is then derived. The conclusion is at the end of the solution presentation rather than at the beginning.

Note that the conclusion is necessarily written at the end of a problem. The conclusion cannot be known before the problem is solved