## Brainteaser 1730: Not so usual

**From The Sunday Times, 12th November 1995** [link]

As usual Eric was early for his morning train. Two express trains of the same length passed through the station in opposite directions, each at its own constant speed. Out of interest Eric timed them and noted that the faster one took 6 seconds to pass him, while the slower one took 8 seconds.

As soon as they had passed he saw his travelling companion, Len, 30 yards along the platform. In his conversation later, Eric told Len that he had been standing exactly in line with the point at which the fronts of the trains coincided.

Len then commented that, by coincidence, he had been standing exactly in line with the point at which the ends of the trains coincided. Eric was delighted because he was now able to work out the speeds of the trains.

How long were the trains?

This puzzle was included in the book *Brainteasers* (2002, edited by Victor Bryant), under the title of “Commuter computer”. The puzzle text above is taken from the book.

[teaser1730]

## Jim Randell 8:11 am

on8 October 2019 Permalink |At time 0s the fronts of the two trains (each of length

xyards) are in line with Eric.At time 6s, the faster train’s end passes Eric. So it is travelling at

(x/6)yards/s.At time 8s, the slower train’s end passes Eric. So it is travelling at

(x/8)yards/s.The ends of the trains pass each other (and Len) at time

t, when the faster train has travelled its entire length plus 30 yards, and the slower train has travelled its entire length less 30 yards.So:

These equations are solved to give:

Solution:The trains were 210 yards long.So the faster train is travelling at 35 yards/s (about 72 mph) and the slower train is travelling at 26.25 yards/s (about 54 mph).

And the ends of the trains passed each other (and Len) 6/7 seconds after the end of the fastest train passed Eric.

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