Algebra

Systems of Equation Fair Race.
Hello, this question relates to Solving Systems of Equations. I was asked to complete a portfolio, here are the directions for said portfolio:

1. Choose two animals with different speeds. You can choose from the chart
that starts at the bottom of this page or do research to choose your own.
2. Design a fair race in which the two animals have an equal chance of winning
if they race at their top speed. Here are a few tips for your design:
a. The race is fair if the two animals could finish the race in the same
amount of time.
b. You can give the slower animal a shorter distance to race.
c. Since this is a video game, the race does not need to be realistic—it
can be any length, and the animals can run at a constant speed.
3. Write a system of two linear equations showing the distance each animal can
travel to model the fair race. Be sure to define all variables.
4. Graph the system to prove that the two animals have an equal chance of
winning the race. Explain how the graph proves the race is fair.

I chose an ostrich with a speed of 40 mph. and a elephant with a speed of 25 mph. I've determined that the equations are as such:
y=40x
y=25x+1.6
And I know that I need to find where the lines of the equations meet on the graph, I just need help solving it, with an explanation so I can better understand it. If anyone would be willing to help me I would be grateful, thank you.

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  1. Since the Left hand sides are equal you can set the right hand sides equal. This is The Comparison method and it is a subset of the Substitution method.
    That is, you are subbing 40x from the first equation into the second equation.
    40x = 25x + 1.6
    and solve for x : )
    once you have the value of x, then sub it back into the first equation and solve for y

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  2. Thank you, this helped me a lot.

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