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The Fly and The Trains

Two trains 150 miles apart are traveling toward each other along the same track.
The first train goes 60 miles per hour.
The second train rushes along at 90 miles per hour.
A fly is hovering just above the nose of the first train.
It buzzes from the first train to the second train, turns around immediately,
and flies back to the first train, and turns around again.
It goes on flying back and forth between the two trains until they collide.
If the fly's speed is 120 miles per hour, how far will it travel?

We want to know the total distance that the fly covers,
so let's use Distance = Rate * Time to solve the problem.
We already know the fly's rate of flight.
If we can find the time that the fly spends in the air,
we can figure out how far it travels.

Ignore the fly for a minute, and concentrate on the trains.
The first train is traveling at 60 miles/ hour and
the second train is going 90 miles/ hour, so they are approaching
each other at 60 miles/ hour + 90 miles/ hour = 150 miles/ hour.
Now we know the rate at which the trains are closing in on each other
and their distance apart (150 miles), so we can find the time until they crash:
Distance = Rate * Time
Time = Distance / Rate
= (150 miles) / (150 miles/ hour)
= 1 hour.

The fly spends the same amount of time traveling as the trains.
It goes 120 miles/ hour, so in the one hour that
the trains take to collide, the fly will go 120 miles.