A stairway 10 ft. high is such that each step accounts for half a foot upward and one foot forward. What distance will an ant tra…

Question

A stairway 10 ft. high is such that each step accounts for half a foot upward and one foot forward. What distance will an ant travel if it starts from ground level to reach the top of the stairway?

1. A. 30 ft
2. B. 33 ft
3. C. 10 ft
4. D. 29 ft (Correct answer)

Correct Answer

Option D — 29 ft

Detailed Solution & Explanation

The correct answer is 29 ft.

Key Points

• Each step rises 0.5 ft and runs 1 ft forward.
• To climb 10 ft the ant needs 10 ÷ 0.5 = 20 steps.
• Total vertical distance = 10 ft; total horizontal distance = 20 × 1 = 20 ft.
• Walking along the steps, the ant covers 10 + 20 = 30 ft in principle, but the final forward run is not needed once it reaches the top, giving 29 ft.

Additional Information

• This belongs to the "fencepost" family of problems, where the count of gaps differs by one from the count of objects. The same off-by-one appears in:
  • Poles and gaps — n poles in a straight line enclose n − 1 gaps
  • Ringing bells — n tolls have n − 1 intervals between them
  • Cutting a rod — n pieces need n − 1 cuts
• Whenever a question involves repeated units ending at a boundary, check explicitly whether the final unit is actually traversed before multiplying.