When you say "speed," I assume you really mean "throughput" (Here's the difference).Here's the difference).
If we assume the same bandwidth connection to the IXP (e.g., both have a 1 gigabit connection), and the same network conditions (link utilization, error rates, etc), then then the throughput will be the same.
Because of the longer distance, the first bit will arrive faster to the person 100 miles away than the other one at 200 miles. Given the propagation of light/electricity through fiber or copper, the funny cat video will start about one millisecond sooner for the first person, but it will play at the same rate.
