Final answer:
Calculating Karl's total distance walked involves adding up the distances covered each day and using given proportions to determine the halfway and three-quarters points. After calculating each segment of the journey and using proportions for the final parts, it appears there is an inconsistency as the answer does not match any of the given options. There may be an error in the question's data or interpretation.
Step-by-step explanation:
The question asks us to find out how far Karl walked from Starton to Endham. To do this, we'll use the information provided about his daily distances and calculate the total distance of his journey. The key steps include determining the distance walked on each day, finding out the halfway point, calculating the remaining distance, and using the proportions given to find the total distance traveled.
On the first day, Karl covered 12 km. On the second, third, and fourth days, he walked 45 km each day. Therefore, in four days, Karl walked: 12 km + 3 * 45 km = 147 km. By the fifth day, Karl had reached halfway through the journey, which means twice 147 km is the total distance, giving us 294 km. With three-quarters of the journey completed by the end of the eighth day, we multiply 294 km by ¾ to get 220.5 km. This is the distance covered by the end of the eighth day. By the ninth day, Karl covered three-fifths of what was left, and on the last day, he did the remaining 36 km.
Let's denote the total remaining distance after the eighth day as R. On the ninth day, Karl covers ⅓ R, and on the tenth day, the remaining 36 km. So, we have:
- R = ⅓ R + 36 km
- R - ⅓ R = 36 km
- ⅕ R = 36 km
- R = 36 km × ⅕
- R = 60 km (remaining distance after eighth day)
To find the total distance (T), we add the distance covered in the first eight days to the remaining distance:
T = 294 km (distance by the end of the fifth day × 2) + 60 km R
T = 294 km + 60 km
T = 354 km
This answer is not among the provided options, which suggests there might be an error either in the question's data or in the interpretation of the question. Therefore, we cannot determine with certainty which of the provided options (A, B, C, or D) is correct, based on the information given and calculations above.