In order to qualify for the finals in a racing event, a car must achieve an average speed of 270 Km/h on a track with a total length of 1410 m. If a particular car covers the first half of the track at an average speed of 232 km/h, what minimum average speed must it have in the second half of the event in order to qualify? The correct answer is 322.887 km/h.

This is a matter of applying the principles that v = d/t and t = v/d. The overall average speed is 1.41 Km/(Total_time), and Total_time is the sum of time for each of the two segments. Note that I convereted the distances to Km for consistency. The time needed for the first segment is 0.705/232, and the time needed for the second segment is 0.705/x, where x is the speed in question. So you have:


v_{avg} \ = \ \frac {1.41} {TotalTime} \ = \ \frac {1.41} {\frac {0.705} {232} + \frac {0.705} x}


Now solve for x. Hope this helps.

Werido