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Ruben is driving along a highway that passes through Barstow. His distance d, in miles, from Barstow is given by the equation
d = |210 − 60t|,
where t is the time, in hours, since the start of his trip and
0 ≤ t ≤ 5.
When will Ruben be exactly 90 miles from Barstow?

Respuesta :

sqdancefan

Answer:

  • after 2 hours, and
  • after 5 hours

Step-by-step explanation:

Given that Ruben's distance from Barstow is d = |210 -60t|, you want to know the time t when he is exactly 90 miles from Barstow.

Setup

The absolute value will be 90 when the argument of the function is either -90 or +90.

The question resolves to two equations:

  • 210 -60t = -90
  • 210 -60t = 90

Solution

These two-step linear equations can be solved in the usual way:

  • -60t = -300 . . . . subtract 210
  • -60t = -120

Then ...

  • t = -300/-60 = 5 . . . . divide by the coefficient of t
  • t = -120/-60 = 2

Ruben is 90 miles from Barstow after driving 2 hours, and again after driving 5 hours.

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