Final answer:
The relative velocity of the second runner with respect to the first is 0.70 m/s, and the second runner will win the race, finishing approximately 49.17 meters ahead of the first runner.
Step-by-step explanation:
To figure out who runs the fastest, we calculate (a) the relative velocity of the second runner compared to the first, (b) determine who will win the race based on their current velocities and distances to the finish line, and (c) find out what distance ahead the winner will be when crossing the finish line.
The relative velocity of the second runner with respect to the first runner is calculated by taking the difference between their velocities. Since the second runner has a velocity of 4.20 m/s and the front runner has a velocity of 3.50 m/s, the relative velocity is given by 4.20 m/s - 3.50 m/s, which equals 0.70 m/s.
To determine who will win the race, we compare the time it will take for each runner to reach the finish line. The time for the front runner to finish is 250 m / 3.50 m/s = 71.43 seconds. The second runner is 45 m behind and has to cover 250 m + 45 m at a velocity of 4.20 m/s, which will take (295 m / 4.20 m/s) = 70.24 seconds. Since 70.24 seconds is less than 71.43 seconds, the second runner will win the race.
When the second runner crosses the finish line, the front runner will still have 0.70 m/s * 70.24 s = 49.17 m to go. Therefore, the second runner will be approximately 49.17 meters ahead when crossing the finish line.