Final answer:
The time to complete an auto race with 8 laps, where the first 2 laps are at an average speed of 190 mph and the remaining 6 laps at 200 mph, is found through the expression T = 2d / 190 + 6d / 200, where d is the length of one lap. Option B, 2d / 190 + 6d / 200, correctly represents this time in terms of d.
Step-by-step explanation:
To find the time it takes the driver to complete the race in terms of d, which is the length of one lap, we need to calculate the time taken for each segment of the race and then add them together. Since time is equal to distance divided by speed, we can express the total time for the race as the sum of the time for the first two laps and the time for the remaining six laps.
The driver completes the first 2 laps at an average speed of 190 miles per hour. Thus, the time taken for the first two laps, t1, is given by:
t1 = 2d / 190
For the remaining 6 laps, the driver maintains an average speed of 200 miles per hour. The time taken for these laps, t2, is:
t2 = 6d / 200
The total time, T, to complete the race is the sum of t1 and t2:
T = t1 + t2
Hence, the expression for the total time in terms of d is:
T = 2d / 190 + 6d / 200
The correct option from the given choices is B) 2d / 190 + 6d / 200.