Question

Two trains are traveling toward each other on the same track, each at 60 miles per hour. when they are exactly 120 miles apart, a fly takes off from the front of one of the trains, flying toward the other train at a constant rate of 100 miles per hour. when the fly reaches the other train, it instantly changes directions and starts flying toward the other train, still at 100 miles per hour. it keeps doing this back and forth until the trains finally collide. if you add up all the distances back and forth that the fly has travelled, how much total distance has the fly travelled when the trains finally collide?

Answer 1

Answer:

What you have given here is not practically possible to calculate…as fly speed and train speed is no match. As per your statement, train is traveling slower than a fly.

Step-by-step explanation:

Still you mentioned that speed of train is 60 miles per hour.

Two trains travelling in opposite direction with same speed.

If we forget the fly part, then to cover the distance 120 miles between them…each one will take one hour time to reach half the distance and they will collide.

Now the other factor of fly comes into existence…

A fly takes from one train towards second one with speed 100 miles an hour. Note this speed is 40 miles per hour more than the speed of the train. That means if the fly flies with this speed, in one hour it would have covered a distance of 100 miles. But as the second train is moving with speed 60 miles an hour so it is obvious that even before the fly reaches a distance of 80 miles, it would have met the train.

Now it travels back to first train with same speed 100 miles an hour. But this time the distance is only 40 miles between the train. So before it reaches the first train, they would have already collided.

This means that the fly can only manage one forth and one back distance before the two trains collide.

…there is no maths to this.

Answer 2

100 miles is the total distance traveled when the trains finally collide.  

Given:

Speed of train is 60 miles per hour.  

Speed of the another train 100 miles per hour

To find:

Total distance has the fly traveled when the train finally collides = ?

Solution:   

Two trains travelling in opposite direction with same speed.

If we forget the fly part, then to cover the distance 120 miles between them

Each one will take 1 hour time to reach half the distance and they will collide.  

[Time to collide= total distance/total speed$=\frac{120}{60+60}= 1hour$]

Now the other factor of fly comes into existence…

A fly takes from one train towards second one with speed 100 miles an hour.

Difference between speed of fly than the speed of the train $=100-60 = 40$miles per hour.

That means if the fly flies with this speed, in one hour it would have covered a distance of 100 miles. But as the second train is moving with speed 60 miles an hour so it is obvious that even before the fly reaches a distance of 80 miles, it would have met the train.

Now it travels back to first train with same speed 100 miles an hour. But this time the distance is only 40 miles between the trains. So before it reaches the first train, they would have already collided.

This means that the fly can only manage one forth and one back distance before the two trains collide.

Time taken by train to meet = time taken by bird to fly $=\frac{d i s t a n c e}{s p e e d}$

$\begin{array}{l}{\frac{120}{(60+60)}=\frac{D}{100}} \\ {D=100 \text { miles }}\end{array}$

100 miles is the total distance traveled when the trains finally collide.