John is at a car show. Beginning 2.5 miles away, a car travelling at a constant 45 miles per hour approaches and then passes John. The distance between John and the car can be represented by the equation d = |2.5 – 45t|. At what times is the car 0.5 miles from John?
Can someone please help me solve this? What are the steps in solving it? Thanks! (=
Please can someone help me!? (=
Am i suppose to give you the answer
Can you help me with the steps to solve it?
To solve this problem, we need to find the times at which the distance between John and the car is 0.5 miles.
First, let's substitute 0.5 for 'd' in the equation:
0.5 = |2.5 - 45t|
Next, we need to solve the absolute value equation by considering both the positive and negative cases:
Positive case: 0.5 = 2.5 - 45t
Negative case: 0.5 = -(2.5 - 45t)
Let's solve the positive case:
0.5 = 2.5 - 45t
Subtracting 2.5 from both sides:
-2 = -45t
Dividing by -45:
t = 2/45 ≈ 0.0444
Now, let's solve the negative case:
0.5 = -(2.5 - 45t)
Expanding the expression:
0.5 = -2.5 + 45t
Adding 2.5 to both sides:
3 = 45t
Dividing by 45:
t = 3/45 ≈ 0.0667
So, the possible times at which the car is 0.5 miles from John are approximately 0.0444 and 0.0667.