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?
let the total distance of the race be 2x miles.
time taken by Ryder = x/110 + x/130 = 13x/1430 + 11x/1430
= 24x/1430 = 12x/715
= appr .01678x
Carter's time = 2x/120 = appr .01667x
So who won?
To determine who won the race, we need to compare the total distances covered by Speedy Ryder and Cannonball Carter.
We can calculate the distance covered by Speedy Ryder by first finding the distances covered in the two halves of the course separately, and then adding them together.
Let's assume the total distance of the course is D miles.
For the first half, Speedy Ryder averaged 110 miles per hour. The time taken to cover the first half can be found using the formula:
Time = Distance / Speed
So, the time taken by Speedy Ryder to cover the first half of the course is:
Time_first_half = (D/2) / 110
For the second half, Speedy Ryder averaged 130 miles per hour. The time taken to cover the second half can be found similarly:
Time_second_half = (D/2) / 130
Now, let's compare the times taken for each racer.
Since Cannonball Carter maintained a constant speed of 120 miles per hour throughout the race, the time taken by Cannonball Carter to cover the entire distance is:
Time_Cannonball_Carter = D / 120
If Speedy Ryder's total time (sum of time for the first and second half) is less than Cannonball Carter's time, then Speedy Ryder won the race. Otherwise, Cannonball Carter won the race.
Therefore, the winner of the race depends on comparing these times.