A jet pilot plans to cover a 1000mi course at an average speed of 1000mph. For the first 800 mi the speed is 800mph. At what rate must the remaining distance be covered. no ans given

well I did it this way(since it is an average)

$\displaystyle \frac{\frac{800}{1} + \frac{200}{h}}{2}=\frac{1000}{1}$

$\displaystyle 800+\frac{200}{h} =2000$

$\displaystyle 800h + 200 = 2000h$

$\displaystyle 200 = 2000h-800h $

$\displaystyle \frac{200}{1200} = h$

$\displaystyle h = \frac{1}{6}$ or $\displaystyle 1200$mph for the rest of the $\displaystyle 200m$

just seems there would be a shorter way