Problem Description Sheet:       Crossing the River             

Introduction: Several groups of people are on the west side of a river and wish to cross to the east side (as shown in the picture below). Each group of people has a boat that can hold a maximum of 100 kg. All people in the group are able to paddle the boat. The river is deep and cold and none of the people can swim well.

Problem:

  1. An 80 kg man and a 40 kg youth are at point A with a boat that holds a maximum of 100 kg. Explain or show that it is impossible for them to get across to point A.

  2. A 60 kg woman and two 35 kg children are at point B with a boat that holds a maximum of 100 kg. Explain or show how they can all get across to point B by having the boat cross the river three times.

  3. An 80 kg man and two 40 kg youth are at point C with a boat that holds a maximum of 100 kg. Explain or show how they can all get across to point C.

  4. Two 80 kg adults and three 40 kg youth are at point D with a boat that holds a maximum of 100 kg. Explain or show how they can all get across to point D.

Materials: pencil, paper, calculator 

Extra Question: For each additional 40 kg youth that joins the group at point D, how many extra trips are needed? How many extra trips are needed for each additional 80 kg adult?

 

Topic(s):

Numbers and operations
(N-39, P-4c), critical and creative thinking, communication

 Activity Type:

  Group  Individual 

Assessment:

  Scale:      Levels 1-5        

  Self  Peer  Teacher 

  Include in your portfolio?
  Yes  No  Optional 

  Toward your marks?
  Yes  No  Optional 

 

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