Carlo walks over a railway bridge. At the moment that he is precisely ten meters away from the middle of the bridge, he hears a train coming from behind. At that moment, the train, which travels at a speed of 25 m/s, is exactly as far away from the bridge as the bridge measures in length.

Without hesitation, Carlo rushes straight towards the train to get off the bridge. In this way, he misses the train by precisely four meters. Had Carlo rushed exactly as fast in the other direction, the train would have hit him eight meters before the end of the bridge.

What is the length of the railway bridge?

There are two scenarios: Carlo runs towards the train, or runs away.  Call the time elapsed in each of these scenarios T1 and T2, respectively.  Let B = the length of the bridge.

The distance the train travels in T1 is B - 4.  The distance the train travels in T2 is 2B - 8.  Thus, T2 = 2*T1.

The distance Carlo travels in T1 is B/2 - 10.  The distance Carlo travels in T2 is B/2 + 2.  Combining this with the fact that T2 = 2*T1, we can solve for B which produces a solution of 44 meters.

Posted by tomarken on 2014-03-13 09:02:01