Question

A race car completes a lap on a 1600 m long track with an average speed of 250 km/h. If the car's average speed on the first half of the track was 225 km/h, what was its average speed on the second half?

 

 km/h

Answer 1

The average speed is total distance over total time:

$$v_{av}=\frac{D}{T}=\frac{D}{D/(2v_{av1})+D/(2v_{av2})},\\\space\\ v_{av}=\frac{2v_{av2}v_{av1}}{v_{av2}+v_{av1}},\\\space\\ v_{av2}=\frac{v_{av}{v_{av1}}}{2v_{av1}-v_{av}}=\frac{250·225}{2·225-250}=281.3\text{ km/h}.$$