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Meeting Trains

Problem

Two railway stations, $P$ and $Q$, are 279 miles apart.
A train departs from $P$ at 2pm and travels at a constant speed of 51 mph towards $Q$.
At 3pm a second train begins a journey from $Q$ towards $P$ at a constant speed of 60 mph.

How far apart are the two trains twenty minutes before they pass each other?


Solution

As twenty minutes is one third of an hour, each train will have travelled a distance of $51/3 = 17$ and $60/3 = 20$ miles respectively in the twenty minutes before they pass each other.

Hence they must have been $17 + 20 = 37$ miles apart.

Problem ID: 261 (29 Jan 2006)     Difficulty: 1 Star

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