Lesson
This lesson is merely an application of quadratic equations to problem solving, and more particularly using the quadratic formula to solve these equations.
Study the example used in the Focus since it outlines the steps you should follow in problem solving. These are repeated below for emphasis.
Step 1 : Summarize the Situation ( Use diagrams or tables if they help )
Step 2 : Decide How to Solve the Problem
Step 3 : Set up an Equation that can be Solved
Step 4 : Solve the Equation ( Use the method that you find the easiest )
Step 5 : Interpret the Solution to the Equation in Context
If you would like to view another example of this 5 step problem solving click on "b" below.
Example
Dave and Art are moose hunting when Dave spots a moose in the distance. Dave sprints towards the moose with Art starting 1 minute behind him since he dropped the magazine belonging to his gun. Art doesn't worry since he knows that he can run 1 km/h faster that Dave. If he overtakes Dave in 500 meters, what is the average speed of each in km/h ?
Solution
Step 1 : Summarize the Situation
Note the units in the problem; all units must be the same throughout your calculations. Therefore, the 500 meters should be written as 0.5 kilometres.
This problem is a good example of summarizing the information in a table:
Hunter |
Distance |
Average Speed |
Time |
Dave |
0.5 |
x |
|
Art |
0.5 |
x + 1 |
|
Since Art started 1 minute later and time is in hours, we write their difference in times as 
hours.
Step 2 : Decide How to Solve the Problem
Set up an equation that shows the relationship between the difference in time for each hunter.
Step 3 : Set up an Equation that can be Solved
Since their difference in time is hours , we have the equation
Step 4 : Solve the Equation
After it is simplified to be a quadratic equation, you may use any of the methods available to you to solve the equation including graphing, factoring or the quadratic formula.
Follow the steps to solve the equation by clicking on the Go forward one frame button below and navigate by using the Global Actions buttons. Read and follow each step:
Step 5 : Interpret the Solution to the Equation in Context
Since a negative speed doesn't make sense in this situation x = -6 is an inadmissible root and x = 5 is the only solution.
Dave's speed is 5 km/h and Art's is 6km/h
Activity
Focus questions p.52. Complete 34, 35 and 36
Think About p.50 and p.51
Check Your Understanding p.52 - 55. Complete 37 to 50 inclusive
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
After you do the assigned activities, click on the Test Yourself button at the top of the page for a quick quiz on this lesson.
Test Yourself
Find a quadratic equation to model the following problem and solve by using the quadratic formula.
To save fuel on a 240 km trip to Gander the Harnum family reduced their usual speed by 20 km/h. This made the trip 1 hour longer than usual. What was the slower speed for the Harnums ?