If the inner planet has a speed v, and its orbit has a radius r and period T, what is the speed and radius of the outer planet if its orbital period is 2T?

T is proportional to r^3/2 so r is proportional to T^2/3.
Doubling T means the second planet has a radius of r * 2^2/3

v = 2πr / T

Doubling T and increasing r by a factor of 2^2/3 means the second planet has a speed of v * 2^-1/3