## Solution to: Train Trouble

Let the length of the bridge be *x* meters.

Running towards the train, Charles covers 0.5*x*-10 meters in the time that the train travels *x*-4 meters.
Running away from the train, Charles covers 0.5*x*+2 meters in the time that the train travels 2*x*-8 meters.

Because their speeds are constant, the following holds:

(0.5x-10) / (x-4) = (0.5x+2) / (2x-8)

which can be rewritten to

0.5x^{2}- 24x+ 88 = 0

Using the quadratic formula we find that *x*=44, so the railway-bridge has a length of 44 meters.

Back to the puzzle