Final answer:
Runner A will be 115.2 meters away from the starting point at time t = 45 seconds, while Runner B will be approximately 120.7 meters away, assuming they continue at their calculated constant speeds of 2.56 m/s and 2.84 m/s, respectively.
Step-by-step explanation:
The question is asking us to calculate how far Runner A and Runner B will be from the starting point at a certain time, given that they are running at constant speeds. Both runners reached a distance of 64 meters from the starting point at 25 seconds into the race. We need to determine their speeds and then use those speeds to calculate their positions at 45 seconds.
Since Runner A starts at time t0 seconds and Runner B starts at 2.5 seconds, we can assume t0 = 0 seconds for simplification. Therefore, Runner A's speed is 64 meters divided by 25 seconds, which equals 2.56 m/s. Runner B, starting at 2.5 seconds, covers 64 meters in 22.5 seconds (because they reach 64 meters at the same time), so their speed is approximately 2.84 m/s.
To find how far each runner will be from the starting point at t = 45 seconds, we multiply their speeds by 45 seconds. Runner A will be 2.56 m/s * 45 s = 115.2 meters away. For Runner B, we must account for their delayed start by adding 2.5 seconds to the total time, so they run for 42.5 seconds. Runner B will be 2.84 m/s * 42.5 s = approximately 120.7 meters away from the starting point.