Problem 56 - Algebra A Combined Function

Question

According to federal regulations, a wheelchair ramp should rise no more than 1 foot for a horizontal distance of 12 feet. Write the slope as a grade. Round to the nearest tenth of a percent.

Step-by-Step Solution

Answer

The slope as a grade is 8.3%.

Step 1: Write the Slope in Fraction Form

The slope of a ramp is the ratio of the vertical rise to the horizontal run. Given that the vertical rise is 1 foot and the horizontal run is 12 feet, the slope as a fraction is \( \frac{1}{12} \).

Step 2: Convert Fraction to Decimal

To convert the slope \( \frac{1}{12} \) into a decimal, divide 1 by 12. This gives \( 0.0833 \) (rounded to four decimal places for accuracy).

Step 3: Convert Decimal to Percent

To convert the decimal \( 0.0833 \) to a percentage, multiply by 100. This gives \( 8.33\% \).

Step 4: Round to the Nearest Tenth of a Percent

Round \( 8.33\% \) to the nearest tenth of a percent. The nearest tenth of a percent is \( 8.3\% \).

Key Concepts

Slope Calculation

Understanding how to calculate the slope of a wheelchair ramp is crucial for ensuring accessibility according to regulations. The slope is essentially the steepness of a ramp, and it's usually written as a ratio of the vertical rise to the horizontal run. In this situation, if a ramp rises by 1 foot for every 12 feet of horizontal distance, we express this as a slope using the fraction \( \frac{1}{12} \).
This fraction tells us that for every foot of vertical height, the ramp extends 12 feet horizontally. It's important to note that a smaller slope ratio indicates a less steep ramp, which is more accessible for wheelchair users.
To develop a stronger understanding, think of slope calculations like walking up an inclined plane. The more gradual the incline (lower slope), the easier it is to ascend. To sum up, writing the slope in fraction form helps to quickly understand and compare it with required standards.

Percent Conversion

Sometimes, it's useful to represent a slope or ratio as a percentage. It can make the information more intuitive. Converting a slope from a fraction to a percentage involves a few simple steps:
1. Start by converting the fraction to a decimal. This is done by dividing the numerator by the denominator. In the problem, the calculation is \( \frac{1}{12} = 0.0833 \).
2. Next, to make this decimal a percentage, multiply the decimal by 100. This transforms the decimal form \( 0.0833 \) into \( 8.33\% \).
3. Finally, round the percentage to the nearest tenth for simplification. For example, \( 8.33\% \) rounds to \( 8.3\% \).
This conversion process is essential in many contexts because percentages are often easier for people to understand than fractions or decimals.

Federal Regulations for Ramps

Federal regulations play a key role in ensuring that building features like ramps are accessible for everyone, including people with disabilities. Regulations like the Americans with Disabilities Act (ADA) set specific requirements for the slope of wheelchair ramps.
According to these federal guidelines, the maximum permissible slope is \( \frac{1}{12} \). This means that for every foot of rise, the ramp must have at least 12 feet of run. Translated to a percentage, this is approximately \( 8.3\% \).
Why is this important? A steeper slope could make it difficult or unsafe for individuals using wheelchairs to navigate the ramp. Compliance with these federal regulations not only helps in creating accessible environments but also ensures safety and independence for individuals relying on wheelchairs.
By adhering to these rules, architects and builders contribute to a more inclusive society where all individuals can access public and private spaces efficiently and comfortably.