6) Starting from 50 miles away, a car drives toward a speed checkpoint and then passes it. The
car travels at a constant rate of 30 miles per hour.
The distance of the car from the checkpoint is given by d=|50-30t|.
At what times is the car 5 miles from the checkpoint?
To find the times at which the car is 5 miles from the checkpoint, we can set up and solve the equation:
|50 - 30t| = 5
This equation represents the absolute value of the difference between the car's distance from the checkpoint (d) and 5.
We can solve this equation by considering the two cases where either 50 - 30t = 5 or 50 - 30t = -5.
Case 1: 50 - 30t = 5
Subtract 50 from both sides of the equation:
-30t = -45
Divide both sides by -30 (remembering to flip the inequality sign since we are dividing by a negative number):
t = 3/2
Case 2: 50 - 30t = -5
Subtract 50 from both sides of the equation:
-30t = -55
Divide both sides by -30:
t = 11/6
Therefore, the car is 5 miles from the checkpoint at times t = 3/2 hours and t = 11/6 hours.