Question

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?

Answer 1

• after 2 hours, and
• after 5 hours

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.