To determine the winner of the race between the tortoise and the hare, we need to calculate the total time each competitor takes to complete the 1000 meters. Let's break down their journeys step by step.
The Tortoise's Journey
The tortoise moves at a steady speed of 0.2 meters per second for the entire distance of 1000 meters. To find out how long it takes, we can use the formula:
Plugging in the values:
- Distance = 1000 meters
- Speed = 0.2 m/s
Calculating the time:
- Time = 1000 m / 0.2 m/s = 5000 seconds
The Hare's Journey
The hare's journey is a bit more complex due to the nap. Let's break it down into two segments:
First Segment: The Initial 200 Meters
The hare runs the first 200 meters at a speed of 2 m/s. Using the same formula:
- Distance = 200 meters
- Speed = 2 m/s
Calculating the time for this segment:
- Time = 200 m / 2 m/s = 100 seconds
Nap Time
After running, the hare takes a nap for 1.3 hours. We need to convert this time into seconds:
- 1.3 hours = 1.3 × 3600 seconds = 4680 seconds
Second Segment: The Last 800 Meters
Finally, the hare runs the remaining 800 meters at an average speed of 3 m/s:
- Distance = 800 meters
- Speed = 3 m/s
Calculating the time for this segment:
- Time = 800 m / 3 m/s ≈ 266.67 seconds
Total Time for the Hare
Now, we can sum up all the time segments for the hare:
- Time for first segment: 100 seconds
- Nap time: 4680 seconds
- Time for second segment: 266.67 seconds
Total time for the hare:
- Total Time = 100 + 4680 + 266.67 ≈ 5046.67 seconds
Comparing the Times
Now that we have the total times for both competitors:
- Tortoise: 5000 seconds
- Hare: 5046.67 seconds
To find out who wins and by how much time, we subtract the tortoise's time from the hare's time:
- Time difference = 5046.67 seconds - 5000 seconds ≈ 46.67 seconds
Final Outcome
The tortoise wins the race by approximately 46.67 seconds. This classic tale emphasizes the value of perseverance and steady effort over speed and overconfidence. In this case, the tortoise's consistent pace allowed it to finish the race ahead of the hare, despite the hare's initial speed advantage.
