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Paisley and Damian are both driving along the same highway in two different cars to
a stadium in a distant city. At noon, Paisley is 315 miles away from the stadium and
Damian is 383 miles away from the stadium. Paisley is driving along the highway at a
speed of 42 miles per hour and Damian is driving at speed of 59 miles per hour. Let
P represent Paisley's distance, in miles, away from the stadium t hours after noon.
Let D represent Damian's distance, in miles, away from the stadium t hours after
noon. Write an equation for each situation, in terms oft, and determine whether
Paisley or Damian is closer to the stadium 5 hours after noon.
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Respuesta :

Using linear functions, it is found that:

  • Paisley's equation is: P(t) = 315 - 42t.
  • Damian's equation is: D(t) = 383 - 59t.
  • Damian is closer to the stadium 5 hours after noon.

What is a linear function?

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value.

Paisley is 315 miles away from the stadium, and driving at a speed of 42 miles per hour, hence for the linear equation for his distance after t hours, we have that:

m = -42, b = 315, then:
P(t) = 315 - 42t.

Damian is 383 miles away from the stadium, and driving at a speed of 59 miles per hour, hence for the linear equation for his distance after t hours, we have that:

m = -59, b = 383, then:

D(t) = 383 - 59t.

After 5 hours, their distances are:

P(5) = 315 - 42(5) = 105

D(5) = 383 - 59(5) = 88

D(5) < P(G), hence Damian is closer to the stadium 5 hours after noon.

More can be learned about linear functions at https://brainly.com/question/24808124

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