Functions project... Help!

Question

For an upcoming project I have to pretend to create a virtual race as a spinoff if the Tortoise and the Hare. The animals I am using are an elephant (25 mph) and a mouse (8 mph). I have to write a system of two linear equations showing the distance each animal can travel to model a fair race. The mouse can travel a shorter distance and the animals can run at a constant speed. The race can be any length, no matter how unrealistic. I then have to graph the system to prove that the two animals had an equal chance of winning. 

 

I do not understand these instructions. I do not understand how to make a linear equation with this information and how to graph it. Can somebody please walk me through the instructions so I can finish my project and better understand what the teacher is asking? Thank you!! 

Answer 1

Claire, what is a linear equation?? It's an equation where x and y grow or shrink at constant rates.

 

For example, if a plant grows a half inch a week, if h = the height and t = the time, h = (1/2)t.

 

This equation means that the plant grows at 1/2 inch EVERY week. If the plant grows 3/4 inch one week, the equation no longer works and we don't have a linear relationship.

 

Remember that distance = rate x time. You are looking for both the distance and the time where the two would meet. Set up your two equations with the two variables, modeling them after the equation above.

 

Since the distances are the same, you can set the two right sides equal to each other and solve for t. Then substitute that value into either equation to solve for d.

 

You should know how to graph a line. Think y = mx + b. Since the distance depends on the time, time will be your x-axis and distance will be your y-axis. Where your two graphed lines meet is your answer for what fits your two equations.