In a grand prix automobile race, Speedy Ryder averaged 110 miles per hour for the first half of the course and 130 miles per hour for the second half of the course. Cannonball Carter maintained a constant speed of 120 miles per hour throughout the race. Who won the race?

Speedy

d at 110 and d at 130
t = d/110 + d/130 = d(.01678)

Cannon
2 d at 120
t = 2 d/120 = d/60 = d(.01667)

Speedy's time is bigger, he lost

To determine who won the race, we need to compare the times it took for both Speedy Ryder and Cannonball Carter to complete the race.

Let's start by calculating the time it took for Speedy Ryder to complete the race.

Since Speedy Ryder's speed was 110 miles per hour for the first half of the race, and the race course is divided into two equal halves, we can assume that each half is the same distance. Let's call the length of each half "d" miles.

For the first half of the race, Speedy Ryder traveled at a speed of 110 miles per hour, so the time it took for him to cover the distance "d" can be calculated using the formula: time = distance / speed. Therefore, the time for the first half of the race is t1 = d / 110.

Similarly, for the second half of the race, Speedy Ryder traveled at a speed of 130 miles per hour. The time it took for him to cover the distance "d" can be calculated as t2 = d / 130.

Therefore, the total time taken by Speedy Ryder to complete the race is t_total = t1 + t2 = d / 110 + d / 130.

On the other hand, Cannonball Carter maintained a constant speed of 120 miles per hour throughout the race. For him, the time taken to cover the entire distance "2d" of the race course is t_cannonball = (2d) / 120.

Now, by comparing the total time taken by Speedy Ryder (t_total) and the time taken by Cannonball Carter (t_cannonball), we can determine who won the race.

If t_total is less than t_cannonball, Speedy Ryder won the race. Otherwise, if t_total is greater than t_cannonball, Cannonball Carter won the race.

Therefore, by using the given information about the speeds of Speedy Ryder and Cannonball Carter, and applying the above calculations, we can determine who won the race.