What distance does a geo-synchronous satellite have to be from earth

Assume that it takes 90 minutes for a satellite near the Earth's surface to orbit around Earth of radius RE.
What distance does a geo-synchronous satellite(i.e. has a period around the Earth of 24 hours) have to be from Earth?
1. 3RE
2. 16RE
3. 6RE
4. 24RE
5. 13RE

An explanation for this would be great. I'm stumped. Thanks!

Remember from Kepler's laws that for the same parent body, the square of the period is proportional to the cube of the semi-major axis.

T^2 ~ R^3

24 hours contains 16 90-minute periods. The new period is 16 times longer, so T^2 is now 256 times longer.

What increase in R would make the right-hand-size 256 times larger? The cube root of 256.

cuberoot(256) ~ 6.3

So the satellite would need to orbit 6.3 RE from the center of the earth.

Kepler's Third Law. T^2 is proportional to R^3.

You know that you want T to be 24 hours. Take the ratio of 24 hours to 90 minutes. Square it. That's the ratio of R^3, so take the cube root. That's the ratio of R to RE.