Boat Trips

							                               Boat Trips

Four friends go on a picnic. They have to cross a river,
but there is only one boat for hire and it can only hold
three people.

How many trips back and forth across the river will be
required to move the four people to the other side ?

Remember that the boat cannot return on its own.

You can use diagrams, use a table like the one below or even act out
the parts to check your answers.


            waiting to cross   journey    on the other bank
          --------------------------------------------------
                4                 0                 0
                1                 3 
                                                    3
                                   1               2
                2
                0                  2
                                                    4
          --------------------------------------------------
              total number of journeys for 4 people = 3




How many trips are need to carry 20 people on a picnic
over the river ?

Try this with different numbers of people.
Can you find a rule which tells you the number of trips if
you know the number of people to be carried ?

Answers


 number of people   4   5   6   7   8   9 10 11 12 13 14 15 16 17 18 19 20
--------------------------------------------------------------------------------------
 number of trips    3   3   5   5   7   7   9   9 11 11 13 13 15 15 17 17 19


If the number of people crossing the river is odd, the number of trips is two less than
the number of people.

If the number of people crossing the river is even, the number of trips is one less than
the number of people.