Problem of the Fortnight #3

SPLAT!

We all know the story about Casey Jones marching into the cabin, the two trains on one track, and the inevitable train wreck, but did you know that a certain hyper-heroic insect was present during this drama as well? That’s right, a certain Ms. Squito was desperately flying back and forth between the two trains trying to warn the engineers of both trains of the looming tragedy – alas, to no avail! However, this incident has spawned a rather interesting question – how far did Ms. Squito fly during this fateful episode? OK, let’s get a bit more specific. Casey Jones’s train left the Chicago station and traveled at a velocity of 48.7 mph up to the moment of impact with the other train. The other train left Indianapolis (181.3 miles from Chicago) exactly one hour after Casey left Chicago, driven by an apparently nameless engineer, and traveled at a constant speed of 58.2 mph up to the moment of impact. Ms. Squito began at Casey’s train when he left Chicago and flew at 82 mph (a really, really hyped up squitter!) throughout the drama. Upon reaching the train from Indy, Ms. Squito instantaneously reversed course and flew toward Casey’s train at the same 82 mph. Once Ms. Squito got to Casey’s train, she again instantaneously reversed course and repeated this trip over and over until becoming the first victim of this legendary tragedy. What was the total distance that Ms. Squito flew before being squashed to the atomic level by many tons of forged metal?

Please be sure to include detailed explanations and justifications.

Solutions are due by 4pm on Friday, October 8^th in Goodrich 108