## March 21, 2011

### A Fly In Between Trains Problem

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?

Kumar said...

fly has traveled 100 miles.

Vinu said...

100 miles

Anonymous said...

the trains will collide after i hour. so the fly travels 100 miles

Rahul said...

100 miles is right less the length of the fly.

Anonymous said...

200 miles

Anonymous said...

There is no way a fly could generate enough force to break out of the airstream around a train... so it doesnt.

Jaa'Moka said...

Vipin said...

100 miles..............imagine Trains A and B.....using relative speed concept....lets have B stationary. So relative velocity of A wrt B is 60-(-60) = 120 miles per hour. So it will take Train A (120/120) = 1 hr to collide with Train B. So total distance covered by the fly in 1 hr is 100 miles.

Anonymous said...

200 mph ..back and forth

Anonymous said...

60 mph each..and the distance to collide is 120mph.. 60x2=120
120mph/60mph=2
fly travels 100mph..so
100mphx2=200mph back and forth..
i therefore conclude the fuckin fly can only travel back and forth..
>>200MPH<<

Anonymous said...

ahmmm.. maybe the fly would be dead ih it hits the other train..haha LOL...

Thangbrand said...

A genetically engineered fly is flying at 100MPH. at a train that is moving tward it at 60MPH.
in 45 minuets the fly would have covered 75 miles.
In 45 minuets the train coming at it would have covered 45 miles.

75+45=120 miles

What was the last thing to go through the fly's mind as he hit the windsheild?

Thangbrand said...

But then the fly turns and heads for the other train. In the remaining 15 minuets the fly covers
25 more miles for a total of

120+25= 145 total miles befor the trains collide.

Thangbrand said...

OOPS! 75+25 = 100 miles.

Anonymous said...

It's irrelevant that the fly is going back and forth - as long as it doesn't stop moving we can just assume it's going at the rate of 100MPH for the amount of time it takes the trains to collide.

The two trains moving closer at 60MPH each means 120MPH closer together, for 120 miles, makes one hour of time.

Visa via, ergo, the fly moves at 100MPH for one hour.

----------: :------------
60 m/h 120 60 m/h

in 1 hr. train colide

fly speed is 100 m/h

after 30 min fly is 50 m far from 1st train
and 2T is 30 m far from 2nd train

still gap is of 40 m

again after 15 mins fly is total 75 m far from 1st train
2T is total 45 m far from 2nd train

so now fly will change direction once traveled 75 m in 45 min.

Then in reamining 15 min Fly will travel back for 25 m and train will colide

So toatl distance covered by Fly is 100 mile

in 1 hr. train colide

fly speed is 100 m/h

after 30 min fly is 50 m far from 1st train
and 2T is 30 m far from 2nd train

still gap is of 40 m

again after 15 mins fly is total 75 m far from 1st train
2T is total 45 m far from 2nd train

so now fly will change direction once traveled 75 m in 45 min.

Then in reamining 15 min Fly will travel back for 25 m and train will colide

So toatl distance covered by Fly is 100 mile

Anonymous said...

So me, I. Went all technical with this question and my answer was.. well let's just say the fly traveled about 98.5 miles before the trains colided. I could be wrong though