A speed ramp at an airport is a moving conveyor belt on which you can either stand or walk. It is intended to get you from place to place more quickly. Suppose a speed ramp is 120 m long. When you walk at a comfortable speed on the ground, you cover this distance in 86 s. When you walk on the speed ramp at this same comfortable speed, you cover this distance in 35 s. Determine the speed at which the speed ramp is moving relative to the ground.

Options

A. 3.4 m/s
B. 1.4 m/s
C. 2.0 m/s
D. 2.4 m/s

Answer

To determine the speed at which the speed ramp is moving relative to the ground, we can break down the problem into a series of steps.

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( V_c \) be the comfortable walking speed of the person (in m/s).
- Let \( V_r \) be the speed of the ramp (in m/s).
- The length of the ramp, \( d = 120 \) m.

2. **Calculate Comfortable Walking Speed on Ground:**
- When walking on the ground, the person covers 120 m in 86 s.
\[ V_c = \frac{d}{t} = \frac{120 \, \text{m}}{86 \, \text{s}} \approx 1.395 \, \text{m/s} \]

3. **Calculate Total Speed on the Ramp:**
- When walking on the ramp, the person covers 120 m in 35 s.
- The total speed while walking on the ramp is the sum of the person's walking speed and the ramp's speed:
\[ V_c + V_r = \frac{d}{t} = \frac{120 \, \text{m}}{35 \, \text{s}} \approx 3.429 \, \text{m/s} \]

4. **Set Up the Equation:**
- From the two equations, we have:
\[ V_c + V_r = 3.429 \, \text{m/s} \]
\[ V_c = 1.395 \, \text{m/s} \]
- Substituting \( V_c \) into the first equation gives:
\[ 1.395 + V_r = 3.429 \]

5. **Solve for Ramp Speed \( V_r \):**
- Rearranging the equation:
\[ V_r = 3.429 - 1.395 \approx 2.034 \, \text{m/s} \]

6. **Conclusion:**
- The speed of the ramp relative to the ground is approximately \( 2.034 \, \text{m/s} \).

### Final Answer:
The speed at which the speed ramp is moving relative to the ground is approximately **2.03 m/s**.