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Why is the answer "55 minutes, because you're always sending the fastest person across...

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mwhoopee | Student, Undergraduate | eNotes Newbie

Posted March 26, 2012 at 1:47 AM via web

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Why is the answer "55 minutes, because you're always sending the fastest person across the river" in this Discrete Mathematics word problem?

 

The problem as stated in the textbook:  Four people wish to cross a river.  They have a boat, but the boat holds at most two people.  Each person takes a different amount of time to cross the river; person A takes 25 minutes, person B takes 20 minutes, person C takes 10 minutes, and person D takes 5 minutes.  When two people are in a boat, it takes the maximum of their time to cross the river; that is, persons A and C together would take 25 minutes. How long does it take everyone to cross the river.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 26, 2012 at 10:06 PM (Answer #1)

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Four people wish to cross a river.  They have a boat, but the boat holds at most two people.  Each person takes a different amount of time to cross the river; person A takes 25 minutes, person B takes 20 minutes, person C takes 10 minutes, and person D takes 5 minutes.  When two people are in a boat, it takes the maximum of their time to cross the river; that is, persons A and C together would take 25 minutes.

If each person is sent across the river on the boat alone the maximum time it takes for them to cross the river is 25 + 20 + 10 + 5 = 60 minutes.

The least time is taken when A and B cross together and  C and D cross together. In this case the total time taken is 25 + 10 = 35 minutes.

The answer would be 55 minutes if A and B are sent alone and C and D go together.

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