Two trains, initially 540 miles apart, travel towards each other at 80 and 40 mph respectively. A poor wee bird flies frantically backwards and forwards between the trains at a speed of 15mph. How far does the bird fly before it is crushed between the trains?

The easy way to solve this problem is to calculate that the trains meet after 540/(80+40) = 4.5 hours, and so the bird flies 4.5*15 = 67.5 miles.