Avery W.
asked • 12/02/22Comparing two linear functions
Damian and Kayla are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Damian is 900 miles away from the stadium and Kayla is 500 miles away from the stadium. Damian is driving along the highway at a speed of 50 miles per hour and Kayla is driving at speed of 25 miles per hour. Let DD represent Damian's distance, in miles, away from the stadium tt hours after noon. Let KK represent Kayla's distance, in miles, away from the stadium tt hours after noon. Graph each function and determine whether Damian or Kayla is closer to the stadium 14 hours after noon.
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1 Expert Answer
Well, let's see. At 1:00 pm, Damian is 850 miles away. How do I know that? He drive 50 miles closer in that one mile. Every hour, I'm subtracting 50 miles.
y = -50x + 900
Can you find the equation for Kayla, graph both, and get your answer?
Avery W.
The equation for Kayla is -25x+500 and Damian's equation is -50x+900
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12/03/22
Avery W.
My question is, is Damian or Kayla closer to the stadium 14 hours after noon, and how many miles closer?
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12/03/22
Don B.
Those are the right equations, Avery. But the problem statement says D is Damian's distance after t hours and K is Kayla's distance after t hours, so I'll use those symbols. I'll also switch the terms around just for readability: K = 500 - 25t, and D = 900 - 50t. We're interested in where they are 14 hours afternoon, so t = 14. What does that give you for K and for T? Think about it before scrolling down for the answer! Plugging t = 14 into the equations gives: K = 500 - (25*14) D = 900 - (50*14) That gives you the answer. You could also think that Damian starts 400 miles further away but gains 25 miles on Kayla every hour; at that rate, how far ahead or behind will he beafter 14 hours? That gives the same answer. Does that clarify things?
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12/03/22
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Mark M.
Did you graph the functions? What is your question?12/02/22