Fast courts are faster because they're slicker. Slicker surfaces don't grip the ball as much so it just skids off. Because of the lack of grip, the ball doesn't lose as much kinetic energy after the bounce. Also, because the ball skids lower after the bounce, it's because there is less time until the 2nd bounce.
Slow courts are slower because they're griddier. So they grip the ball better and it doesn't skid off as easily. Unless you want a lesson in physics, just accept the griddy court will grip the ball. That grip will cause the ball to lose more kinetic energy so the ball will travel slower after the bounce. That friction causes the ball to bounce higher too. The higher bounce means there's more time until the 2nd bounce.
For simplicity sake, throw the ball across a carpet and hard floor. Which ball will reach its destination assuming you impart the same amount of kinetic energy to both?