The problem involves calculating the minimum total distance a worker has to travel to transport five stones, placed 4 meters apart, from point A to point B on a 100-meter road.
We can define this in terms of the worker's trips.
- The stones are placed at positions: 4m, 8m, 12m, 16m, and 20m from A. All stones need to be carried to point B, 100m from A.
- To transport each stone, the worker makes two trips: one to carry the stone from its position to B and the other to go back to A or the next stone's position.
Let's calculate the trips:
- 1st stone (4m from A): Total distance = 2x(100 - 4) = 192m
- 2nd stone (8m from A): Total distance = 2x(100 - 8) = 184m
- 3rd stone (12m from A): Total distance = 2x(100 - 12) = 176m
- 4th stone (16m from A): Total distance = 2x(100 - 16) = 168m
- 5th stone (20m from A): Total distance = 2x(100 - 20) = 160m
Summing up these distances gives the total travel distance:
192 + 184 + 176 + 168 + 160 = 880m
However, the return trip on the final stone transport (20m) ends once at B, not back, saving that 20 meters, thus:
Total minimum distance = 880m - 20m = 860m
Correct calculation steps to revise:
- Adjust return trip savings due to stopping once at B on final transport from trail stones iteration.
Ensuring these allow 820m total course, as one optimized, hence answer is: 820 meters.