HMMT 2006 A3
- Algebra
- Answer
The train schedule in Hummut is hopelessly unreliable. Train A will enter Intersection X from the west at a random time between 9:00 am and 2:30 pm; each moment in that interval is equally likely. Train B will enter the same intersection from the north at a random time between 9:30 am and 12:30 pm, independent of Train A; again, each moment in the interval is equally likely. If each train takes 45 minutes to clear the intersection, what is the probability of a collision today?
Dataset text NuminaMath olympiads. Quoted with source.
Also HMMT 2006 E7.
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\frac{13}{48}
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