Calculating the distance between 2 stations in a transfer
Calculating the distance is nearly impossible. You would have to send a block of data and measure the time between the last bit sent and the reception of an acknowledge. If you say that processing time is negligible so is transmission time. The delay between reception and acknowledging in the receiving computer is probably an order of magnitude longer than the time the signal takes to go back and forth (shouldn't that be forth and back?). If the distance is 10km a one way would take 50\$\mu\$s. How long would it take to dump a megabyte of data?  

The 100 seconds is unusually long. The amount of data is probably the payload, and you'll have to add some overhead for header and CRC, but if your packets are 1MB long (which is long, for any protocol) the overhead will be far less than 1%. And then it looks like your assumption about negligible times is false.  

edit
OK, let's, for argument's sake, presume processing time is effectively zero. You have to send 128 packets, which take 1 second each to transmit. Let's say distance between the stations is \$D\$, and one-way time \$T\$. Then the transmission of 1 packet takes \$8ms + T\$. The acknowledge take time \$T\$ to go back to station A. So turnaround time is \$8ms + 2 \cdot T\$. The 128 packets take 100 seconds, so  


  \$ 128 \cdot (8ms + 2 \cdot T) = 100s \$  


Solving for \$T\$ gives us  


  \$ T = \dfrac{1}{2} \cdot \left( \dfrac{100s}{128} - 8ms \right) = 0.39s \$


Then  


  \$D = v \cdot T = 2 \cdot 10^8 m/s \cdot 0.39s = 77 \cdot 10^6m = 77 000 km \$


I hope this is a hypothetical problem.