Here's a scenario that involves a foot chase, and how I would handle it.
<Descriptive Portion>
The Courier is running away from a security guard that suspects that she might have stolen some very important data. The Courier is running through a mall, with the security guard in hot pursuit. She jumps over tables, throws chairs behind her, and pushes people out of the way in order to make headway and hopefully put up obstacles for the security guard. The security guard is dodging these obstacles pretty well, but also tries to take a stance to fire his taser at the girl, missing in the process. The Courier makes it to the front door, but the security guard has already called for backup to lock the door. She jams against the door's bar, pushing fruitlessly. Giving up on the front door, she turns and makes a dash for the upper level, hoping to find a way to jump down. The chase continues....
<Rules Portion>
Player is being chased by NPC. Both Player and NPC are human. Player has an Agility of 4, Body of 3, Strength of 3, Gymnastics of 3, and Running of 3. NPC has an Agility of 3, Body of 3, Strength of 4, Gymnastics of 0, and Running of 1. NPC realizes that there's no chance he'll actually catch up to an tackle Player, so he spends an action radioing ahead to lock the doors and get backup on the way. Due to this, the distance between Player and NPC is 5 meters.
Turn 1: Both roll Initiative, and Player gets the higher score. Player rolls Strength + Running to increase her running speed for a turn. She gets 2 hits, giving her an additional 4m of movement this turn. She moves forward 20 meters.
Turn 1: NPC rolls his Strength + Running, getting 3 hits (6m of extra movement). He moves forward 18 meters. At the end of this turn, the Courier is ahead by 7 meters.
Turn 2: Both roll Initiative, and Player gets the higher score. There is a crowd of people, tables, and chairs in front of Player. Player decides to spend the turn making as much headway as possible, while causing delays for her pursuer. Player rolls Agility + Gymnastics to do a parkour-style jump over the table, knocking chairs and people out of the way in the process. She gets 2 hits, enough to cause some chaos behind her. She moves 16 meters (her normal running rate).
Turn 2: NPC now has to deal with the obstacles, so has to succeed at a Running test, rolling Strength + Running against a threshold of 2 hits (the number of hits Player got on her test). NPC gets 1 hit, which reduces his movement rate for the turn to Walking instead of Running. He moves 6 meters forward. Now Player is ahead by 17 meters.
Turn 3: Initiative again, NPC wins. NPC takes a stance and lines up a taser shot (Aimed Shot) and fires. He suffers a modifier to his dice pool for the target running, a modifier for him running, and a modifier for the range. His dice pool is reduced to 3, and he gets 0 hits.
Turn 3: Player hits the gas, using another Sprint action and getting 3 hits. She can move 22 meters this turn, more than enough to ensure that NPC can't catch up any time soon. She's 15 meters from the door, and slams into it at full force. Instead of getting away though, she's hit the locked door and can't get through. The purpose of the NPC using his radio starts to sink in.
And so on.
