So the farther in universe we look, the faster objects appear to be speeding away from each other. But the farther we look, the further back in time were looking as well. So does this mean the universe is actually slowing down as it ages - nearer objects are older and not moving apart as fast as distant objects (star/galaxies)?
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You have a point.
But remember, it is space that is expanding.
I tend to think of space as a giant balloon that is being blown up. If you are a particle near the center of that balloon you would hardly notice. But if you are closer to the balloon itself your wiggle room would be getting increasingly more comfortable.
Its a 4/3 PI R3 thing. And although we are not likely to be at the center of the universe our ability to look at that universe is limited to something like 13.8 billion light years in any direction. Thats what we can see. And it is a sphere inside a much bigger universe.
Dont use any of this to answer questions on your next physics test. It is simply my imagination going crazy with only a fact or two as backup.
But, I just read that the universe is greater than 14.8 billion light years across,times 2.... So was is will light be travelling at a constant soon?
Just remember to take into consideration a major factor which affects our observation, time. The outside of your balloon will be billions of years older than the point in the middle from where you're making your observations.