# 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...

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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### 1 Answer

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.**