## 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