# algebra

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four men qant to cross a bridge. they all begein on the same side. its night and they only have one flash light with them. at most two men can cross the bridge at the same time,and any party who crosses, either one or two people musy have a flashlight wit them.
the flashlight be walked back and forth not thrown etc. each man walks at a different speed. a pair must walk at the pace of the slower man. man one needs one minute to cross the bridge man two needs 2 minutes,man 3 needs 5 minutes,man four needs 10 minutes.
how can all the men get across the bridge in 17 minutes

• algebra -

HINTS:
1--Since only one person can be permanently taken across at a time, we know that there will be 5 trips made in all; 3 trips bringing a person over and 2 trips where 1 person returns to get another person.
2--By definition, one of the trips across must take 10 minutes dictated by "d's" walking time.
3--Logically, "c and "d", will cross together taking 10 minutes to cross over.
4--This leaves "a" and "b", the two people taking the two shortest times, to arrange their crossings in such a way as to consume the remaining 7 minutes.
5--Four trips consuming 7 minutes can only be achieved by 1 + 2 + 2 + 2 = 7, not necessarily in that order.
6--Person "a's" crossing time can only result from "a" traveling alone since if he was traveling with "b", their crossing time would have to be 2 minutes.
7--Therefore, "a" must make one return trip by himself meaning that he must go across with "b" once and return by himself.
8--We now know that "a" and "b" make at least one trip across together taking 2 minutes, "a" makes one trip returning to the starting side, and "c" and "d" make one trip across taking 10 minutes, consuming in all 2 + 1 + 10 = 13 minutes.
9--With 4 minutes left, it is obvious that "b" accounts for the remaining two trips, one over and oneback.
10--It remains for you to determine the order of these crossings and how and when does person "b" make his trips across and back consuming the remaining 4 minutes.

I think you should now be able to arrange the trips in their proper order.

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