If Mr. E is aboard a spaceship traveling near the speed of light the usual reason for the spaceship not going faster than $c$ is the (relativistic) mass of the ship increases without bound, I think. Yet Mr. E says out loud what about the mass of the fuel? When the fuel's (relativistic) mass increases would its potential energy increase enough to compensate for the ship's (relativistic) mass increase?
The other crucial point is that the actual reason for it not going faster than $c$ is the addition of velocity formula prevents you from accelerating above it –  Jim Apr 12 at 5:17
The actual reason for the rocket under consideration not going faster than $c$ (i.e. maximum signal speed) between a given starting gate and a given finish line is of course that the rocket also presents a signal having been sent from starting gate to finish line (and not even necessarily a signal of the highest speed). p.s. Concerning the well-known formula for adding speeds in the same direction it is worth noting that $\frac{u + v}{1 + u \, v} > 1$ for instance if $v > 1 > u > 0$. –  user12262 Apr 12 at 20:44