A Fly In Between Trains

Algebra Level 3

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?(in miles)


The answer is 100.

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3 solutions

Siva Prasad
Nov 11, 2014

The distance between trains = 120 kms

The trains come closer at total rate of 60+60 = 120 miles per hour.

Then the time needed for the trains to collide is 1 hour

In One hour.....

The Fly can fly a distance of 100x1= 100 Miles

And that is the answer

Did the same.

Keshav Tiwari - 6 years, 6 months ago

Since the the two trains have the same speed they will collide after travelling 120 2 = 60 \dfrac{120}{2}=60 miles each. So

t = d V = 60 60 = 1 h o u r t=\dfrac{d}{V}=\dfrac{60}{60}=1~hour .

Then for the fly,

d = V t = 100 ( 1 ) = 100 m i l e s d=Vt=100(1)=100~miles

Jabale Rahmat
Nov 9, 2014

As both of the trains are moving with the same speed of 60 miles per hour so they need 1 hour to collide head to head. Therefore, the fly has only one hour to travel back and forth and as the fly is moving with a speed of 100 miles per hour so, it will move 100 miles in this time.

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