Page 45 - NUMINO Challenge_D2

5 Crossing the River

Basic Concepts Crossing the River

Several people want to cross the river by using a boat that can only carry
one or two people at a time. Each person takes a different length of time to
row the boat. A person who rows slowly takes as much time as when two
people row the boat. In this case, the person who rows the fastest should
move back and forth several times in order for all the people to cross the
river in the shortest length of time.

Example Three people want to cross a river by using a boat that can carry
up to two people at a time. The following shows the time it takes
for each person to cross the river. What is the shortest length of
time it takes for all three people to cross the river?

It takes 10, 15, and 20 minutes for A, B, and C to cross the
river by rowing the boat alone.

When two people are in the boat, they take as much time
to row as a person who rows slowly to cross the river.

There should be one person on the boat to move back and
forth.

Class Notes

Among A, B, and C, the fastest person is . Therefore, should move back and
forth several times.

The method for all three people to cross the river the fastest is:

A and B cross the river together: 15 minutes

A comes back: minutes

A and C cross the river together: minutes

Therefore, the shortest length of time it takes for all three people to cross the river is
minutes.

42 NUMINO Challenge D2