Question

On a straight road AB 100 metres long, five heavy stones are placed 4 metres apart beginning at the end A. A worker starting at A has to transport all stones to B by carrying one stone at a time. The minimum total distance he has to travel is

• A. 960 m
• B. 820 m
• C. 468 m
• D. None of these

Hint:

On a straight road AB 100 metres long, five heavy stones are placed 4 metres apart beginning at theendA.AworkerstartingatAhastotransportallstonestoBbycarrying one stone at a time. The minimum total distance he has to travel is

Answer 1

The Correct Option is B

The problem: Minimize the total distance a worker travels to move five stones from locations along a 100-meter road to point B. Stones are 4 meters apart.

The worker's trips are defined as follows:

1. Stones are at: 4m, 8m, 12m, 16m, and 20m from A. All stones go to B, which is 100m from A.
2. Each stone transport involves two trips: to B and back to A or the next stone's location.

Trip calculations:

• 1st stone (4m): Distance = 2 * (100 - 4) = 192m
• 2nd stone (8m): Distance = 2 * (100 - 8) = 184m
• 3rd stone (12m): Distance = 2 * (100 - 12) = 176m
• 4th stone (16m): Distance = 2 * (100 - 16) = 168m
• 5th stone (20m): Distance = 2 * (100 - 20) = 160m

Total travel distance:

192 + 184 + 176 + 168 + 160 = 880m

The final return trip is to B, not back to A, saving 20 meters.

Total minimum distance = 880m - 20m = 860m

Revised calculation:

• Account for return trip savings from the final stone transport.

Optimized total course: 820 meters.