A commuter exits her neighborhood by driving y miles at r1 mph, then turning onto a central road to drive x miles at r2 mph. Assume that the neighborhood has a xed size, so that xy = c for some number c.
(a.) Find x and y to minimize the time spent driving.
(b.) Show that equal time is spent driving at r1 mph and at r2 mph. This is a design principle for neighborhoods and airports. (See Bejan's Constructal Theory of Social Dynamics.)