Final answer:
The time difference between the two runners when the front runner finishes the race is 32.08 seconds.
Step-by-step explanation:
To find the time difference between the two runners when the front runner finishes the race, we first need to calculate the time it takes for the front runner to reach the finish line. We can use the formula time = distance / velocity. The distance to the finish line is 250 m and the velocity of the front runner is 3.45 m/s, so the time taken by the front runner is 250 m / 3.45 m/s = 72.46 s.
Next, we calculate the time taken by the second runner. The distance between the two runners is 42.4 m, and the velocity of the second runner relative to the first can be found by subtracting the velocity of the front runner from the velocity of the second runner. So, the velocity of the second runner relative to the first is 4.5 m/s - 3.45 m/s = 1.05 m/s. Using the formula time = distance / velocity, the time taken by the second runner is 42.4 m / 1.05 m/s = 40.38 s.
The time difference between the two runners when the front runner finishes the race can be found by subtracting the time taken by the second runner from the time taken by the front runner: 72.46 s - 40.38 s = 32.08 s.