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?
could ..someone help al ittle bit in helpin me understand this
You want to know when the car is 5 miles from the checkpoint, that is, the car could be 5 miles before and 5 miles past the checkpoint.
This is where the absolute value part of the equation comes in, then
|50-30t| = 5
50 - 30t = 5 OR -50 + 30t = 5
-30t = -45 OR 30t = 55
solve these two equations for t to get the two different times
tysm!!
Sure! I'd be happy to help you understand this problem.
To find the times when the car is 5 miles from the checkpoint, we can set up an equation using the distance formula provided.
The distance of the car from the checkpoint is given as:
d = |50 - 30t|
To find the times when the car is 5 miles from the checkpoint, we want to solve for t when d = 5.
So we can rewrite the equation as:
5 = |50 - 30t|
In order to solve this equation, we need to consider two possibilities:
1. When 50 - 30t is positive:
In this case, the equation becomes:
5 = 50 - 30t
To solve for t, we can subtract 50 from both sides:
50 - 5 = 30t
45 = 30t
Dividing both sides by 30, we get:
t = 45/30 = 3/2 = 1.5
So, at t = 1.5 hours, the car is 5 miles from the checkpoint.
2. When 50 - 30t is negative:
In this case, the equation becomes:
5 = -(50 - 30t)
We can simplify this equation by removing the negative sign:
5 = -50 + 30t
Adding 50 to both sides:
55 = 30t
Dividing both sides by 30, we get:
t = 55/30 = 11/6 ≈ 1.83
So, at t ≈ 1.83 hours, the car is 5 miles from the checkpoint.
Therefore, the car is 5 miles from the checkpoint at t = 1.5 hours and t ≈ 1.83 hours.