1. The problem statement, all variables and given/known data This is from Calculus for the Practical Man, by J.E. Thompson, 1962 edition. "Two automobiles are moving along straight level roads which cross at an angle of 60 degrees, one approaching the crossing at 25 mph, and the other leaving at 30 mph on the same side. How fast are they approaching or separating from each other at the moment when each is 10 miles from the crossing?" The chapter is about differentials and, additionally, trigonometry is not allowed. 2. Relevant equations Definition of velocity. Basic differentiation operations. 3. The attempt at a solution I start by finding what time it is since the leaving car left the crossing. At a distance of 10 miles, the time is 1/3 hr. This means the approaching car was at a distance of 10+25/3 miles when the leaving car was at the crossing. So I can calculate the average rate of change between the crossing and 10 mile positions to be 25 mph just by algebra but that's not what its asking. Also, just by thinking about it its obvious they are separating after the time of the equilateral triangle. The answer given is that they are separating at 2.5 mph. I'm sure the answer involves expressing the separation distance as a function of the other distances and then differentiating, but I can't come up with a geometrical rule that helps me. Its also kind of annoying that I can't tell if the angle between the roads should be 60 or 120, or if it is irrelevant in the final analysis.