What is the required speed for the last 2 laps to qualify for the race?

AI Thread Summary
To qualify for the race, the driver must average 180 km/h over four laps. After averaging 150 km/h for the first two laps, the driver needs to maintain a speed of 225 km/h for the last two laps to achieve the required average. The confusion arises from the assumption that the time taken for each half is equal, which is not the case. The average speed calculation must account for total distance and total time, leading to the conclusion that a higher speed is necessary for the final laps. Understanding the relationship between speed, distance, and time is crucial for solving this problem.
Jimbo57
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Homework Statement


"A race car driver must average 180 km/h for 4 laps to qualify for a race. Because of engine trouble, the car averages only 150 km/h over the first 2 laps. What speed must be maintained for the last 2 laps?"


Homework Equations





The Attempt at a Solution


So I do know the answer to be 225km/h but I don't quite understand why. Since half the time trial is completed with the driver being 30km/h below the needed average, wouldn't the 2nd half just be 30km/h above the needed average (210km/h for the last 2 laps)? I'm missing something here.
 
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You r averaging the speed for individual laps.. (150 + v)/2 = 180, and thus v=210

Actually avg. speed = total distance/total time = (150*2d + v*2d)/[2d/150 + 2d/v] = 180

In short you r assuming that he takes equal time to complete the first 2 laps and the last 2 laps, which is incorrect.
 
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