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Two trains are 300 km apart and are approaching each other, each at 60 km/h. A fly leaves the first train towards the second at 90 km/h.
When you touch the second one, it instantly turns and returns to the first, and so on until the trains collide. How many kilometers does the fly travel?
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Answer: 225 km.
Time to crash:
$$ t=\frac{300}{60+60}=2.5\text{ h}. $$
Fly distance:
$$ d=90\cdot2.5=225\text{ km}. $$
It is not necessary to add infinite sections; the total time is enough.
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