A train leaves station A towards B?

Question

There are two train stations: A and B, 180 miles apart.

First train leaves A and travels towards B at 25 miles per hour.
At the same instant, second train leaves B and travels towards A at 35 miles per hour.

There is a fly sitting on the train 1. The moment the train leaves, the fly takes off and flies towards train 2 at 45 miles per hour. As soon as the fly reaches train 2, it makes a U-turn and flies back towards train 1. It reaches train 1, makes a U-turn, and flies towards train 2, etc. etc., until the trains collide and the fly gets squashed.

Question: what's the total distance the fly has travelled?

Answer 1

Ignore the fly for a minute, and concentrate on the trains. The first train is traveling at 25 miles/ hour and the second train is going 35 miles/ hour, so they are approaching each other at 25 miles/ hour + 35 miles/ hour = 60 miles/ hour. Now we know the rate at which the trains are closing in on each other and their distance apart (180 miles), so we can find the time until they crash:

Distance = Rate * Time
Time = Distance / Rate
= (180 miles) / (60 miles/ hour)
= 3 hours

The fly spends the same amount of time traveling as the trains. It goes 45 miles/ hour, so in the three hours the trains take to collide, the fly will go 135 miles.

Answer 2

Time 1 (to get to Train 2) = [180-35*Time 1]/(80)
80*T1 = 180 - 35*T1
T1 = 180/115
T1 = 36/23 hours

Distance 1 ( Distance fly travelled to get to Train B) = 36/23*45 = 70.43 miles

In that time Train 1 has also travelled 36/23*25 = 39.13 Miles

So the difference at the moment the fly turns back is 70.43-39.13 = 31.3 miles

Then T2 = [31.3 - T2*25]/60
85*T2 = 31.3
T2 = 0.368 hours

In that time the fly travelled an additional 16.57 miles

So the total distance travelled for the first round trip is 70.43+16.57 = 87 miles

EDIT: I misread the problem...the 3*45 = 135 miles is the correct answer.

Answer 3

Sorry...
a----------------b 180miles
25+35 = 60miles/hour
So exactly after 3 hours the collision takes place.
So 45*3=135miles is the distance travelled by that poor fly.

Answer 4

sorry i wanna help but i can't drive a train and i didn't got the ticket too