The equation is an adaptation of the standard Distance Formula, Distance=(rate)(time).
t=5 s and t=7.5 s
Practice makes perfect
Starting at 300 feet away, a car is driving towards us at a speed of 48 feet per second. Let's picture the situation.
The distance d (in feet) between us and the car after t seconds is given by the following absolute value equation. Our task is to find out after how many seconds will the car be at the distance of 60 feet away from us.
d = |300-48t|To identify the various parts of this equation, first we need to recognize that this equation is an adaptation of the standard Distance Formula.
Distance=(Rate)(Time)
In the formula r is the rate and t is the time. With this in mind, we can recognize that 48 must be our rate in feet per second, and 300 is the initial distance between us and the car. The reason for the absolute value is that a distance cannot be negative.
d = | 300- 48t|
We can solve for the time(s) when the car is 60 feet away from us by substituting d= 60 into our equation.
d=|300-48t| ⇒ 60=|300-48t|
When solving an absolute value equation, we need to remember to look at both the positive and negative cases.
&Case $1$: 60=300-48t
&Case $2$: - 60=300-48t
Now, we can solve these cases separately. Let's start with the positive case.
Our first solution tells us that the car will be 60 feet away from us when 5 seconds have passed. This is the situation when the car is still behind us. Let's take a look at the other case.
Our second solution tells us that the car will be 60 feet away from us again when 7.5 seconds have passed. This is the case when we are behind the car.
