8.1: Boats in Motion
This activity is intended to supplement Algebra I, Chapter 7, Lesson 2.
ID:11237
Time Required: 15 minutes
Activity Overview
In this activity, students will explore the motion of a boat going up and down the river. They will be instructed to solve the resulting system of equations algebraically and graphically. The transformation graphing application will allow students to explore the slope of a distancetime graph. Additional problems are provided for further practice.
Topic: Linear Equations

Motion,
distance=rate×time  Slope and graphically solving equation
Teacher Preparation and Notes
 The student worksheet provides instructions and question to guide the inquiry and focus the observations.
Associated Materials
 Student Worksheet: Boats in Motion, http://www.ck12.org/flexr/chapter/9617.
Problem 1 – Boat Motion & Graphically Solve
Ask students why the boat goes faster downstream than upstream. They should know that the boat goes with the current downstream making it travel more distance in less time. When the boat goes upstream, it has to fight the current.
1. Downstream rate
2.
3.
Substituting this into either equation gives a distance of
Problem 2 – DistanceTime Graph, Explore Slopes
Using
where
Students should set up lists
On the graph, students are to use the arrows keys to change the rates of the train
To solve this system of equations, students are to distribute and then add the first equation to the second.
The solution is the train moves at
Extension/Homework
1.
So, the speed of the airplane in still air is
2. This problem can only be solved algebraically.
So, the two cars will be
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