Learning Resources

Lesson

This lesson is an application of quadratic equations to problem solving. In most of the problems the quadratic formula is used to solve the resultant equation.

Focus G in your text outlines the following steps that you should follow to solve a problem. 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

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 kilometers. The relationship between distance, rate, and time is given by the formula:

dist = rate x time    or    time = dist/rate

This problem is a good example of how to use a table to summarize information.

Hunter	Distance (metres)	Average Speed (km/hr)	Time (hours)
Dave	0.5	x
Art	0.5	x + 1

Step 2 : Decide How to Solve the Problem

Set up an equation that shows the relationship between the difference in time for each hunter. Since Art started 1 minute later and time is in hours, we write the difference in their times as hours.

Step 3 : Set up an Equation that can be solved

 We thus 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. The solution is shown in the interactive below:

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 x or 5 km/h and Art's speed is (x+1) or 6 km/h.

Activity

1. Read through the example in Focus G on pages 50 - 52 in your text.
2. Complete Focus Questions 34 - 36 on page 52.
3. Do the CYU Questions 37 - 41; 44 - 45; 48 - 50 on pages 52 - 55.

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

• A rectangular piece of sheet metal has a length of 24 cm. All but a square piece at the end is to be electroplated with copper. If the area to be electroplated contains 140 cm² , find the possible widths of the plate.

Solution