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

[Jimbo57]

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.

 

[vanihba]

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.