math
posted by jake .
4 people need to cross a brige but it is dark outside and they only have one flashlight and only 2 people can cross at one time. doris takes 10 minutes bob takes 5 minutes jack takes 2 minutes and annie takes 1 minute. how can thay get across in 17 minutes. someone has to go back with the flashlight.

The key is to have Doris and Bob cross together, after having Annie or Jack waiting on the other side.
Annie and Jack cross last. 
* Let the four people be labeled a, b, c, and d in ascending order of their walking times.
* After reviewing the following hints, you will easily be able to conclude that the minimum crossing time can always be accomplished in T = a + 3b + d minutes which in this case results in T = 1 + 3(2) + 10 = 17 minutes.
* Clearly, one person has to return across the bridge two times with the flashlight to accompany the next person across.
HINTS:
1Since 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.
2By definition, one of the trips across must take 10 minutes dictated by "d's" walking time.
3Logically, "c and "d", will cross together taking 10 minutes to cross over.
4This 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.
5Four trips consuming 7 minutes can only be achieved by 1 + 2 + 2 + 2 = 7, not necessarily in that order.
6Person "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.
7Therefore, "a" must make one return trip by himself meaning that he must go across with "b" once and return by himself.
8We 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.
9With 4 minutes left, it is obvious that "b" accounts for the remaining two trips, one over and oneback.
10It 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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