If you increase your speed while circling Earth, you'll also increase the height of your orbit, which will increase the overall distance you're traveling. It's confusing even for those doing it -- early astronauts employed the "f*****g gun it!" method while attempting to dock with other spacecraft, and missed their mark more often than a nervous kid on prom night.
See, the behavior of an orbiting spacecraft runs almost counter to our earthbound notions of speed and velocity. Again, the orbit itself provides some of the speed because of gravitational force. So to lower your orbit, you need to provide some kind of negative force, in this case, your rockets. But since you're getting closer to Earth -- and gravitational forces are getting stronger -- your kinetic energy actually increases, meaning you're likely to accelerate and f**k up your orbit to high heaven. So when George Clooney increased his speed to travel to the ISS, he almost certainly would have either blasted off into the void or crashed to Earth.
"That doesn't sound right; did you factor the power of my handsomeness into the calculation?"
Buzz Aldrin describes this as the "orbital paradox." And you can't just space jockey your way out of it, it takes more brains than balls. Aldrin, for example, holds a Doctorate of Science in astronautics from MIT. His thesis was "Line-Of-Sight Guidance Techniques For Manned Orbital Rendezvous." Just the title makes our brains hurt.