So a question on how this works. First, the two relevant parts of rules
So with Ride the Lightning as a full round action I can become a living lightning bolt, travel we'll say 300 feet and zap everyone in the way for 15d6 electric, and keep doing it for 15 rounds straight?
That's the gist! But it's worth noting that, line spells, while cool, rarely work more than once per combat. This one may almost be more useful as a transport trick than an attack spell.
Being an uberpowered version of Spring Attack that can deal (minimum) 15d6 for 15 rounds (225d6, an average of 787 damage) with little or no risk of being countered/damaged/stopped, and even less chance of having your target(s) flee, hardly you can say it's not good for attacking. You could storm a castle alone in 90 seconds.
Assuming a base 30' speed with no modifiers (not sure they apply) that is at least 600' feet a round you move.
Actually, for a base speed of 30 feet, that is a maximum of 300 feet."Up to 10 times your speed", doesn't matter if you make double movement, run or whatever. Besides, you couldn't do that, since this kind of movement is itself a full-round action.