SOLUTION: 4 people, starting on the same side, want to cross a bridge. All have to be across in 17 minutes or less. It is night. They have one flashlight, which must accompany them across.

Question 109423: 4 people, starting on the same side, want to cross a bridge. All have to be across in 17 minutes or less. It is night. They have one flashlight, which must accompany them across. A max of 2 people can go at once. The flashlight cannot be thrown. It must be walked back and forth. Each person walks a different speed and pairs must walk together at a rate of the slower person's pace. The 4 persons crossing times are as follows: P1 = 1 min.; P2 = 2 min.; P3 = 5 min., P4 = 10 min. How do you solve this?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
this cannot be done in the allotted time

the fastest person (P1) must accompany each crossing so that the flashlight returns in the shortest time

10+5+2=17 ... but that does not take into account the returning of the flashlight

**ENLIGHTENMENT** ... thanks to Dushenko
the two slowest must cross together to minimize their time impact
... this means the two fastest must cross together leaving a "faster" person on each side to return the light

the two fastest people cross first, one stays and the other returns with the light
... next, the two slowest people cross and the faster returns with the light
... lastly, the two fastest people cross
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