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

Ms Sue, can you help please?

To find the distance Charlie drives, we need to compare the time it takes for both Charlie and Peter to complete the race.

Let's calculate the time it takes for Charlie to complete the race first. We'll use the formula: Time = Distance / Speed.

Let D be the distance Charlie drives. Charlie's average speed is 108 miles per hour. Therefore, the time it takes for Charlie to complete the race is T = D / 108.

Now let's calculate the time it takes for Peter to complete the race. Peter's average speed is 99 miles per hour, and he is given a head start of 12 miles. So the distance Peter drives is D - 12. Therefore, the time it takes for Peter to complete the race is also T = (D - 12) / 99.

Since Charlie and Peter finish at the same time, the times for both of them must be equal. Therefore, we can equate the two equations:

D / 108 = (D - 12) / 99

To solve this equation for D, we can cross-multiply and simplify:

99D = 108(D - 12)
99D = 108D - 1296
9D = 1296
D = 144

Therefore, the distance Charlie drives is 144 miles.

So the answer is 144 miles.