Does a planet's distance from the sun relate to the time it takes to revolve around the sun?

Yes, its all to do with Kepler's third law of planetary motion, which describes the relationship between the orbital period of the plant and the distance of that planet from the sun.

Kepler found that the square of the period, P, is proportional to the cube of the semi-major axis, a (P2 = ka3). The planets orbit the sun in an ellispse, the semi major axis is the longest radius within this ellipse.

Kepler found that a constant k was needed in the equation - this was later found to relate to the mass of the objects. The planets mass is usually a lot less than the star its orbiting, so can often be dropped from the equation.