My friend sets out walking at a speed of $3$ miles per hour. i set out behind her $5$ minutes later at $4$ miles per hour. for how many minutes will my friend have been walking when i catch up to her?

Let the time at which the two friends are at the same distance be x. With this representation, the equation would be,

               3x = 4(x - 5/60)

The value of x from the equation is 0.33, which has a units of hours. Since, we are in minutes.

                  minutes = (0.333)(60)
                  minutes = 20

20 minutes