1. **State the problem:** We need to find a possible whole number length of a race track that rounds to 300 km when rounded to the nearest 100 km and rounds to 250 km when rounded to the nearest 10 km. 2. **Recall rounding rules:** - Rounding to the nearest 100 km means the number is within 50 km above or below 300 km, i.e., between 250 and 349 inclusive. - Rounding to the nearest 10 km means the number is within 5 km above or below 250 km, i.e., between 245 and 254 inclusive. 3. **Find the intersection:** - The length must be in both ranges: - Between 250 and 349 (nearest 100 km rounding) - Between 245 and 254 (nearest 10 km rounding) 4. **Determine possible values:** - The intersection of these intervals is from 250 to 254. - Since the length is a whole number, possible values are 250, 251, 252, 253, or 254. 5. **Write down a possible value:** - For example, 250 km. **Final answer:** $$\boxed{250}$$