Home > Riddles > The mosca between two trenes
Its fame is born from a gentle trick: it seems to ask for an endless sum of twists and turns, when in reality everything is resolved by first setting the key time of the scene.
Two trains are 300 km apart and moving towards each other, each at 60 km/h. A fly leaves the first train towards the second at 90 km/h.
Every time it hits one train, it instantly turns and flies towards the other, repeating the process until the trains collide. What total distance does the fly travel?
Answer: 225 km. Time to crash:
$$ t=\frac{300}{60+60}=2.5\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\text{ h}. $$ Fly distance: $$
d=90\cdot2.5=225\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\text{ km}.
$$ It is not necessary to add infinite sections; the total time is enough.
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