Final answer:
To determine the time for the fox to catch the dog, the relative speed is calculated as 20 m/s (50 m/s - 30 m/s). The time taken for the fox to overcome a 160-meter gap at this relative speed is 8 seconds.
Step-by-step explanation:
To calculate how long it will take the fox to catch up to the dog, we need to consider their speeds and the initial distance between them.
Since the fox is running at 50 meters per second (m/s) and the dog is running at 30 m/s, we find the relative speed of the fox with respect to the dog by subtracting the dog's speed from the fox's speed, which is 20 m/s (50 m/s - 30 m/s).
Now, to find the time it takes for the fox to close the 160-meter gap, we use the formula Time = Distance / Relative Speed. Plugging in the values, we get:
Time = 160 meters / 20 meters per second = 8 seconds.
Therefore, it will take the fox 8 seconds to catch up to the dog.