I have a 99 elantra it seems like it should change out gears quicker than
it does. If you let off the gas it will change out otherwise it take a few
seconds longer.

 

The transmission shifts based on engine speed and vehicle speed (or more
precisely, input and output speed of the trans), and throttle position. I
believe you may have a power-normal button on this car. Check to see if it
is in the normal position. If not, put it there. It is designed to change
the shift points to either a sporty or economy style of driving. Also, if
it won't accelerate properly, you may have your foot depressing the
accelerator more, which will delay shifting to the next higher gear.