Trains leave P for Q, 300 km away, every hour on the hour from 6 a.m., running at 60 km/h. A car leaves Q at 8 a.m. and drives towards P along the line at 90 km/h. How many of these trains does the car meet before reaching P?

Question

Accepted Answer

6. The car is on the road from 8:00 to 11:20. A train that left at hour s meets it at t=6.8+0.4s (solving 60(t-s)=300-90(t-8)). For s=6,7, ,11 this gives 9:12 to 11:12 — all before 11:20; the 12:00 train would need 11:36. So 6 trains.

Trains leave P for Q, 300 km away, every hour on the hour from 6 a.m., running at 60 km/h. A car leaves Q at 8 a.m. and drives towards P along the line at 90 km/h. How many of these trains does the car meet before reaching P?

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