Answer
The driver needs to maintain an average speed of 244 km/h on the last lap.
Work Step by Step
Let $x$ kilometers be the distance of one lap around the track.
Let's find the time $T$ it takes to complete 10 laps at an average speed of 200 km/h.
$T = \frac{10x ~km}{200.0 ~km/h} = 0.0500x ~h$
Let's find the time $t$ it takes to complete 9 laps at an average speed of 196 km/h:
$t = \frac{9x ~km}{196.0 ~km/h} = 0.0459x ~h$
After nine laps have been completed, the time remaining is T-t:
$T-t = 0.0500x ~h - 0.0459x ~h = 0.0041x ~h$
With one lap left, the remaining distance is $x$ kilometers, and the remaining time is: $0.0041x ~h$
To achieve an average speed of 200.0 km/h for all ten laps, we can find the required speed of the last lap:
$v = \frac{x ~km}{0.0041x ~h} = 244 ~km/h$
The driver needs to maintain an average speed of 244 km/h on the last lap.
