Boat Current and Airplane Wind Problems

Boat Current Problem

It takes a boat 3 hours to travel downstream and 7 hours to travel upstream. The speed of the current is 4 km/h.

What is the speed of the boat in still water?

Formula: (rate)(time)=distance

Can you see this in the downstream upstream rectangles shown below?

The blue smooth side of the blocks represent unknown numbers – in this problem we call them b.

b = speed of boat in still water – no current
c = speed of current

across = rate = b + c and b – c
up = time
total rectangle = distance

You can take this problem further and solve for distance. Simply replace the b’s in the downstream upstream rectangles with 10’s and count up the total of each rectangle. The distance is 42 km.

To help children understand the problem draw a picture or create a tangible example of the problem.

Boat Current Problems
– Float a paper or toy boat in water
– Use a bathtub and water to create a stream and current or go outside to a small stream

Airplane Wind Problems
– Fly a paper airplane in the air
– Use a household fan to create wind or go outside on a windy day

Children should always be accompanied by an adult when playing near water or operating an electrical device.

Move from the concrete to the abstract.
– Create a tangible example of the problem
– Draw a picture of the problem
– Build a model of the problem and reshape to solve
– Draw the model
– Write the symbols that represent the model

Use the blocks to introduce higher math concepts to all ages.

Don’t throw all of this at them at one time.
– start with setting up the first rectangles
– then count the over, up, and total of each
– when they are comfortable with this introduce the problem solving steps

The concept stays the same – only the numbers change.
– start off with simple problems – small numbers
– slowly increase the difficulty – bigger and bigger numbers

At the same time students are learning about these higher math concepts they will be honing their basic math skills.