Systems of Equations

Ontario 10 Applied (MFM2P)

Would you win against a lion (Investigation)

Lesson

How do you think you would do in a race against a cheetah or a lion? Systems of equations can be used to find the answer!

- To practice with designing an experiment and collecting data.
- To practice with creating a system of equations to describe a real life situation.
- To understand how to solve a system of equations in multiple ways.
- To review units of length and how to use them properly.

- Ruler
- Stopwatch
- Computer

- Working alone or in small groups, design an experiment that will determine how fast you run. Your units for speed should either be feet per minute, or meters per minute.
- Gather the materials you need according to your experiment design. Complete the experiment and record your data.
- Use your data to determine how fast you run in either feet per minute or meters per minute.
Did you know?
- $1$1 mile = $5280$5280 feet
- $1$1 hour = $60$60 minutes
- $1$1 kilometre = $1000$1000 metres

- Look up the speed of the fastest animal you can think of.
- Convert the units of the animal’s speed to be the same units as your speed (feet per minute or meters per minute). The units on your speed must match the units on the animal’s speed. Use the helpful conversion facts above to help you do this.
- Now use this information to create our first equation. We know that $\text{Distance }=\text{Speed }\times\text{Time }$Distance =Speed ×Time
- Input your speed into this equation. For example, if I found my speed to be $500$500 feet per minute my equation would be $\text{Distance }=500\times\text{Time }$Distance =500×Time . Here, the distance would be measured in feet and the time would be measured in minutes.
- The second equation we will create will be slightly different. We want to give you a slight head start in the race so it’s fair. In order to do this we will use the following equation $\text{Distance }=\text{Speed }\times\left(\text{Time }-\text{Delay Time }\right)$Distance =Speed ×(Time −Delay Time )
- So for example, say I chose a panther as my animal and I have determined that its speed in feet per minute was $3080$3080 ft/min. If I choose to have the panther start $10$10 minutes after I begin the race, my second equation would be $\text{Distance }=3080\times\left(\text{Time }-10\right)$Distance =3080×(Time −10).
- Now that you have both equations, solve the system of equations graphically by graphing the two equations on the same graph. In your graph, time will be on the $x$
`x`-axis and distance will be on the $y$`y`-axis. - Verify the solution you found for the system of equations by using either the substitution method or the elimination method to solve the system.
- You can repeat this process to see how you would do in a race against other animals as well!

- How long did it take the animal to catch up to you? How far did you get before the animal it caught up?
- Do you think this distance would change if you increased the amount of time the animal had to wait before beginning the race? If so, by how much would it change? How do you know?
- Compare with a friend! How far did they make it in their race before the animal they chose caught up with them? Was it farther than you made it racing against your animal? What may be some reasons for you and your friend reaching different distances?

Solve problems that arise from realistic situations described in words or represented by given linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method