Suppose two comets, comet A and comet B, were orbiting the Sun, having the same average orbital radii. If comet A had a higher eccentricity than comet B, which comet would, during some portion of its orbit, have the highest orbital speed?

It is given that comet A has higher eccentricity than comet B and according to Kepler law planet orbit around the sun with the sun as the focus.

An implication of Kepler's law is that the planet moves faster when it close to the sun and slower when distant. This is the result of the conservation of angular momentum.

A has a more elliptical path thus it will be closer to the sun and therefore A will have the highest orbital speed.