Tough one guys! Try this one!?

Question

Two trains are 200km from each other and are each moving at a speed of 50 km/hr towards one another. From one of the trains, a fly takes off, flying straight to the other train at a speed of 75 km/hr. Once the fly reaches the other train, it instantaneously returns back to the other train. The fly continues this back and forth flying until the trains collide into each other and squish the bug. How far did the fly travel before it's death? How many times did the fly land (do not count the fly's starting position as a landing)?

Answer 1

The first part is easy: the trains have a net closing velocity of 100 km/hr and are 200 km apart, so they close in 2 hours, during which time the fly was always travelling at 75 km/hr (it's a VERY fast fly), so it flew 150 km.

On a particular leg, if the trains start a distance x km apart, the closing speed of the fly and the opposite train is 125 km/hr, so it takes x/125 hours, and the trains are (100x/125) = 4x/5 km closer, so the separation at the end of the leg is x/5. So the separation after one leg is 200/5 = 40 km, after two legs 8 km, after three 8/5 km, ..., after n legs it is 200 / 5^n, which is always positive; that is to say, the fly makes infinitely many landings in the last microsecond before the collision.

Of course, what this really says is that there is a finite landing and turnaround time which we've neglected and which will determine the correct answer for this part. ;-)

(I must admit, I'm a bit disturbed that two trains collide head-on, but we're mostly worried about a fly that got squashed in the collision!)

Answer 2

if you'll try to make a figure to show this problem, you'll find that the fly will reach the other train(B) after 1hr and 36 min,thus traveling a total of 120km(trains,travelled 80kms).this time the distance between train A and the fly is 40km(1/5 of original distance)...this will go on,forming a geometric series where a=200 and r=1/5...if you get the sum, you'll get 250,but only 3/5 of this was travelled by the fly,(i.e. 75/(50 + 25), hence the fly travelled 150 km.also note that the fly will take 2 hours of flying,as well as the train to collide...the number of landing that fly will take will be impossible to tell since the geometric series is infinite.

Answer 3

Given the statement of the problem, the fly travels 150 km (2 hr @ 75 kph), and lands an infinite number of times before the trains collide. Change the turn-around to a finite time instead of instantaneous, and you can solve for a finite number of landings.

Answer 4

hmmm.
if the trains were 200 km apart, and each going 50 km and hour, then they each covered 100 km in 2 hrs. and closed the gap between them. In 2 hrs. the fly could have gone 150 km.

i dont know. thats all i could come up with.
wouldnt the fly really only be going 25 km/hr faster than the train? since the fly goes 75 mph and the train goes 50mph? i think the fly landed only once.

Answer 5

There is an easy way to do this problem.
The trains collide in 2 hours, and the fly flies at 75km/hour, so the fly flies for 2 hours, so it flies 150 km. I have no idea how many times it landed though. Maybe 2 or 3? lol

Answer 6

The fly flied 150 km before its death (im sure about this)
and i think the # of landings should be infinite but in real life that isn't exactly possible...(not sure about this part)

Answer 7

That's hilarious..it can't go to the next train..well the fly can't repel the opposite force(wind) outside the train no matter what! hahaha

Answer 8

I would guess that, after being on moving trains, the flies would be in hell (or wherever flies go). But that's just my guess.

Answer 9

I can hook your mom to become more tough