Question

A bank needs to upgrade its ATM kiosks to be wheel-chair accessible. An ATM kiosk entrance has four steps rising up to reach the floor level of the kiosk. Each step is 1000 mm in length, 300 mm in breadth, and 150 mm in height. The bank proposes to create a wheel-chair accessible ramp with a slope of 1:12, adjacent to the steps. What is the minimum horizontal length of the ramp in metre? \

Hint:

In word problems, first identify the information that is crucial for the calculation and ignore any extraneous details. Always pay close attention to the units required for the final answer and perform conversions carefully.

Answer 1

Step 1: Understanding the Concept:
The problem requires calculating the horizontal length (run) of a wheelchair ramp given its total vertical rise and the required slope. The dimensions of the steps are provided to determine the total vertical height the ramp must ascend.

Step 2: Key Formula or Approach:
The slope of a ramp is defined as the ratio of the vertical rise to the horizontal run:
\[ \text{Slope} = \frac{\text{Vertical Rise}}{\text{Horizontal Run}} \] \ We are given the slope and need to calculate the horizontal run after finding the total vertical rise.

Step 3: Detailed Explanation:
1. Calculate the Total Vertical Rise:
There are 4 steps, and each step has a height of 150 mm.
\[ \text{Total Vertical Rise} = \text{Number of steps} \times \text{Height per step} \]
\[ \text{Total Vertical Rise} = 4 \times 150 \text{ mm} = 600 \text{ mm} \] \ This is the total height the ramp must cover.
2. Calculate the Horizontal Length (Run): \ The required slope is 1:12, which means the ratio \(\frac{\text{Rise}}{\text{Run}}\) must be \(\frac{1}{12}\). \ \[ \frac{1}{12} = \frac{\text{Total Vertical Rise}}{\text{Horizontal Length}} \]
\[ \frac{1}{12} = \frac{600 \text{ mm}}{\text{Horizontal Length}} \]
Rearranging the formula to solve for the Horizontal Length:
\[ \text{Horizontal Length} = 12 \times 600 \text{ mm} \]
\[ \text{Horizontal Length} = 7200 \text{ mm} \]
3. Convert the Length to Metres: \ The question asks for the length in metres. Since 1 metre = 1000 mm: \ \[ \text{Horizontal Length in metres} = \frac{7200 \text{ mm}}{1000 \text{ mm/m}} = 7.2 \text{ m} \] \ The length (1000 mm) and breadth (300 mm) of the steps are extra information not needed for this calculation.

Step 4: Final Answer:
The minimum horizontal length of the ramp is 7.2 metres.