The equation shows the relationship between a planet’s orbital period, t, and the planet’s mean distance from the sun, a, in astronomical units, au. if planet y is k times the mean distance from the sun as planet x, by what factor is the orbital period increased?

Basically, this deals with Kepler's Third Law: T^2 = r^3
Let's suppose Planet Y is twice as distant as Planet X.
So, if we increase the distance by a factor of "k", then "r" becomes:
2^2 = r^3
r = cube root (4)
r = 1.587401052

Source:
http://www.1728.org/kepler3a.htm