Charlie and Peter are driving around a racetrack. Charlie drives at an average speed of 108 miles per hour. Peter drives at an average speed of 99 miles per hour. Peter is given a head start of 12 miles. Charlie and Peter finish at the same time. How far does Charlie drive?
126,132,144 or 156 miles
Charlie drives 9 mph faster, and it takes him 12/9 = 4/3 hours to catch up. He drives (4/3)*108 = 144 miles in that time
To find out how far Charlie drives, we need to figure out the time it takes for both Charlie and Peter to complete the racetrack. We can use the formula distance = speed × time to solve this problem.
Let's start by finding the time it takes for Peter to complete the racetrack. Peter's average speed is 99 miles per hour, and he is given a head start of 12 miles. So, the total distance Peter needs to cover is the length of the racetrack minus his head start.
Let's assume the length of the racetrack is D miles. Peter needs to cover D - 12 miles.
To find the time it takes for Peter to complete the racetrack, we can divide the distance he needs to cover by his average speed:
Time for Peter = (D - 12) / 99
Now, let's find the time it takes for Charlie to complete the racetrack. Charlie's average speed is 108 miles per hour, and we assume he starts from the same point as Peter. So, the distance Charlie needs to cover is the length of the racetrack.
Time for Charlie = D / 108
We are given that Charlie and Peter finish at the same time, so their times must be equal:
(D - 12) / 99 = D / 108
To solve this equation and find the value of D, we can cross-multiply:
108(D - 12) = 99D
108D - 1296 = 99D
108D - 99D = 1296
9D = 1296
D = 1296 / 9
D = 144
Therefore, the length of the racetrack is 144 miles. Charlie drives the same distance as the length of the racetrack, which is 144 miles.
Thus, the correct answer is 144 miles.