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?
Please help me solve this! What are the steps in solving it? Please help?! Thanks! (=
so |2.5 - 45t| = .5
2.5 - 45t = .5 OR -2.5 + 45t = .5
-45t = -2 OR 45t = 3
t = 2/45 hrs or t = 3/45 hrs
which is 2 2/3 minutes or in 4 minutes
To find the times when the car is 0.5 miles from John, we need to set up an equation and solve for t.
Step 1: Set up the equation:
We are given the equation d = |2.5 – 45t|, where d represents the distance between John and the car.
Step 2: Set d to be 0.5 miles:
Substitute d with 0.5 in the equation:
0.5 = |2.5 – 45t|
Step 3: Solve for t:
To solve for t in this equation, we need to split it into two separate equations using the positive and negative values of the absolute value.
Case 1: 2.5 - 45t > 0, (Removing the absolute value sign):
Solve for t in this case by isolating the variable:
2.5 - 45t = 0.5
Subtract 2.5 from both sides:
-45t = -2
Divide both sides by -45:
t = -2 / -45
t = 2/45
Case 2: 2.5 - 45t < 0, (Multiplying the inequality by -1 and changing the direction of the inequality):
Solve for t in this case using similar steps:
-2.5 + 45t = 0.5
Add 2.5 to both sides:
45t = 3
Divide both sides by 45:
t = 3 / 45
t = 1/15
Step 4: Finalize the solution:
The car is 0.5 miles from John at t = 2/45 and t = 1/15.
Therefore, the car is 0.5 miles from John at two different times: 2/45 hours and 1/15 hours after the car starts approaching John at the car show.