SOLUTION: I was assigned a problem that reads: "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 des

Algebra ->  Equations -> SOLUTION: I was assigned a problem that reads: "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 des      Log On


   

Question 1110070: I was assigned a problem that reads:
"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:
•The race is fair if the two animals could finish the race in the same amount of time.
•You can give the slower animal a shorter distance to race.
•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.
The two animals that I chose were animal 1 = cheetah (70mph) and animal 2 = Lion (50mph)
I chose a race of 350 miles and the lion gets a 100 mile start
the equations I have using slope intercept form are:
animal 1 - cheetah - 350=70x
animal 2 - lion - 350 50x+100
y=distance of the race
m-speed of the animal
b=hours
Can you help me and tell me if I am on the right track and how I would graph this? I am struggling with how to graph this. When I try to graph it using the slope intercept I get the same line. How do I do this differently? Or what do I do to create a graph using the equations (if Im correct)??
Thank You for your assistance and guidance

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The two animals that I chose were animal 1 = cheetah (70mph) and animal 2 = Lion (50mph)
I chose a race of 350 miles and the lion gets a 100 mile start
the equations I have using slope intercept form are:
animal 1 - cheetah - 350=70x
animal 2 - lion - 350 50x+100
y=distance of the race
m-speed of the animal
b=hours
Can you help me and tell me if I am on the right track and how I would graph this? I am struggling with how to graph this. When I try to graph it using the slope intercept I get the same line. How do I do this differently? Or what do I do to create a graph using the equations (if Im correct)??
Thank You for your assistance and guidance
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You get the same line because you are graphing time.
time = distance/rate
cheetah time = 350 miles/70 mph = 5 hrs
lion time = (350-100)miles/50 mph = 250miles/50mph = 5 hrs
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To get more variability the equation would have to DETERMINE
the distance the lion would have to travel so the game would be fair
OR the speed of one of the animals to make the game fair.
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If cheetah is 70 and distance is x solve for x if time is 5 hrs
If lion is 50 and time is 5 hrs what is his required advantage for a fair game.
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Cheers,
Stan H.
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