A stairway of 20 ft height is such that each step account for half a foot upward and one foot forward. What distance will an ant travel if it strats from ground level to reach the top of the stairway ?

Options

A. a.59
B. b.60
C. c.58
D. d.None of these

Answer

To solve the problem, we need to determine the total distance an ant will travel when climbing a stairway that is 20 feet high, with each step accounting for half a foot upward and one foot forward.

### Step-by-Step Solution:

1. **Determine the Number of Steps**:
- Each step raises the ant by \( \frac{1}{2} \) foot.
- To find the total number of steps needed to reach a height of 20 feet, we can use the formula:
\[ \text{Number of steps} = \frac{\text{Total height}}{\text{Height per step}} = \frac{20 \text{ ft}}{\frac{1}{2} \text{ ft}} = 20 \times 2 = 40 \text{ steps} \]

2. **Calculate the Forward Distance**:
- Each step also moves the ant forward by 1 foot.
- Therefore, the total forward distance traveled by the ant is:
\[ \text{Total forward distance} = \text{Number of steps} \times \text{Distance per step} = 40 \text{ steps} \times 1 \text{ ft/step} = 40 \text{ ft} \]

3. **Calculate the Upward Distance**:
- The total upward distance traveled by the ant is equal to the height of the stairway, which is 20 feet.

4. **Calculate the Total Distance Traveled**:
- The total distance traveled by the ant is the sum of the upward distance and the forward distance:
\[ \text{Total distance} = \text{Total forward distance} + \text{Total upward distance} = 40 \text{ ft} + 20 \text{ ft} = 60 \text{ ft} \]

### Final Answer:
The distance the ant will travel to reach the top of the stairway is **60 feet**.

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