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Algebra Word Problem - Crossing a bridge with a flashlight.

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The band U-2 has concert that starts in 17 minutes and they must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them across to the other side . It is night there is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown.

Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace:
Bono: 1 minute to cross
Edge: 2 minutes to cross
Adam: 5 minutes to cross
Larry: 10 minutes to cross

Can you get them across in 17 minutes?

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Solution Summary

A word problem is solved for crossing a bridge with a flashlight. Members of a group walking at different speeds are determined.

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No, it is impossible

In the direction forward, everybody has to spend at least his stated time, but the person that goes back to bring the flashlight for the next crossing forward should be the fastest.
Therefore, Bono should shuttle forward and back with the flashlight.
The detailed schedule with the fastest possible time is as follows:

Bono (with the flashlight) and Larry cross forward and spend 10 minutes
Bono hurries back with the ...

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