Question on Treadmill & Elliptical

how long should you be on a treadmill or bike or elliptical?

It depends on intentisty, Health, age, weight and goals.

Your goal weight is WAY too low. You don't need to lose any weight, so make sure you eat more to make up for exercising.

It really depends on your age, weight and intensity, like giggle_puppy said.
However, I agree with Phoenix in that your goal weight is too low. If you were 115 and 5'8, you would be underweight, which isn't healthy for a growing 16 year old.
Maybe you should adjust it to 125-130 to see how you look from there, because you don't want to be 110 and have no muscle to speak of!