Crossing the Bridge

Joe, Jill, Brian and Wendy have to catch a train that leaves in 15 minutes. The railway station is the other side of a river. It is dark. Swimming is out of the question but there is a rather fragile bridge. The bridge only holds two persons at any one time and one of them must carry a torch. There is only one torch. Joe can get over the bridge in one minute. Jill takes two minutes. Brian can make it over the bridge in 5 minutes and it takes Wendy 7 minutes to cross. When two persons cross the bridge they have to walk at the pace of the slowest person. How do the four of them manage to catch the train?

ANSWER scroll down a bit further!

1. Joe and Jill cross in 2 minutes
2. Jill returns with the torch in 2 minutes - total of 4 minutes
3. Brian and Wendy cross in 7 minutes - total of 11 minutes
4. Joe returns with the torch in 1 minute - total of 12 minutes
5. Joe and Jill cross again in 2 minutes - total of 14 minutes
All four are safely across with a whole minute to spare!

Thanks to Richard Birkill, Roy Bickler and John Stafford for their answers. Roy Bickler won the draw.

It could be argued that either solution is flawed, on the ground that it does not take into account the time taken to reach the solution.

We may suppose that Joe is the ablest, and could reach the solution in one minute. But he would then need some time (three minutes, say) to persuade the others.

There would be various arguments (in the dark, with only one torch). Some would prefer the intuitive solution, that Joe (the swiftest) should escort each crossing - leading to an elapsed time of 16 minutes or more. The frail Wendy would try to insist that she was escorted by the agile Joe, rather than the less adequate Brian; Brian would take offence, but would eventually be overruled.

And so on ...

So after an extra four minutes (or possibly much more) we may imagine the proposed solution being put into effect.

At time 15, when the train departs, Jill will be on her way back across the river to collect Joe. She will see the train go, containing Brian and Wendy (now not on speaking terms) and calls “goodbye”; realising that she cannot be heard above the noise of the train and the raging torrent beneath her, the best she can do is to wave the failing torch at them..

Jill then struggles back to the stranded Joe, and complains to him “I told you it woudn't work”.

Are they condemned to spend the rest of their lives together on the wrong side of the river?

Tragic!

John Stafford.

Thanks, John, for that enlivened version.

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