Luka Crnkovic wrote: > > Everybody has heard the problem: > > Two trains 200 miles apart are moving toward each other; > each one is going at a speed of 50 miles per hour. > A fly starting on the front of one of them flies back and forth > between them at a rate of 75 miles per hour. It does this until the > trains collide and crush the fly to death. What is the total distance > the fly has flown? > > The solution is simple, using s=t*v, but is ther another way > of solving it by trough limit? >
Sure. I'll set the problem up, and you can finish it. Pick one of the trains as you reference point, and draw the graphs T(t), and f(t). T(t) is the train's distance from you versus time, and f(t) is the fly's versus time. Find the distance the fly travels in the first cycle, from your train to the other and back to you, call it D1. Because of the constant speeds in the problem, the graphs of T(t) is a negative-sloped line from (0,T(0)) to (tf,0). The graph of f(t) is an infinite series of similar triangles. From the parameters of the problem you can find a proportionality constant that relates the distance of the second cycle, D2, to D1. D2=cD1. So the total distance the fly travels is sum(n=1,oo)D1*c^n.