Question

(Apex 2.2.4 math 8) PLEASE I'M SO LOST

The entrance to an accessibility ramp is at ground level.
The first section of the ramp covers a horizontal distance of 18 feet and rises to a landing 1.5 feet above the ground.
The second section of the ramp begins at the landing. It rises at a slope of
\frac{1}{18}
and covers another 9 feet of horizontal distance to reach the door.

Answer the questions to compare the sections of the ramp.
1. What is the slope of the ramp from the ground to the landing? Write your answer as a fraction with a whole-number numerator and denominator.
2. Is the steeper part of the ramp from the ground to the landing or the landing to the door? Explain how you decided which part of the ramp is a steeper.
3. Slope is equal to rise divided by run. If you know the horizontal distance (run) and the slope, how can you find the vertical distance (rise)?
4. What is the vertical distance (rise) from the landing to the door? Show your work.
5. What is the total height of the door above the ground?

Answer 1

Answer: 1.) The slope of the longer ramp is 1/12

2.) The longer ramp from the ground to the landing is steeper. 1/12 is steeper than 1/18. A graph of the slope shows this. See attachment.

3.) If you know the run, you can find the rise by multiplying the run by the slope.

4.) The rise from the landing to the door is 1/2 foot or 6 inches.

5.) The total height of the door above the ground is 2 ft or 24 inches.

Step-by-step explanation: Sometimes it helps to draw a sketch of the info given then make notes as you find solutions. (See in attachments)

1.) 1:5/18. Multiply by 2/2. It becomes 3/36. simplify to 1/12

4.) Multiplying 9ft by 1/18

It's the same as dividing 9÷18= 0.5 ft. OR  9 feet is 108 inches. 108÷18 = 6 inches

5.) Given height, ground to landing: 1.5 ft plus calculated  0.5ft = 2 ft.

OR 18 inches + 6 inches = 24 inches

Answer 2

The answers to questions comparing the sections of the Ramp are;

1) Slope = 1/2

2)The first section of the ramp is steeper because it has a greater slope.

3) Multiply the horizontal distance by the slope.

4) Vertical distance from landing to the door = 0.5 ft

5) Total height of the door above the ground = 2 ft

We are given that;

Height of landing above the ground = 1.5 ft

Horizontal distance of first section of ramp to landing = 18 ft

Horizontal distance of second section of ramp from landing to door = 9 ft

Slope of Second section of ramp = 1/18

I have attached an image showing the ramp alongside the given data;

With these given data, let's proceed to answer the question;

• 1) Slope is defined as ratio of change in vertical height to change in horizontal distance.

From the attached image, we see that for the first section;

vertical height = 9 ft

horizontal distance = 18 ft

Thus, slope = 9/18 = 1/2

• 2) The slope for the first section is 1/2 = 0.5.

The slope for the second section is 1/18 = 0.056

The slope of the first section is greater than that of the second

section and thus we will say the slope of the first section is steeper.

• 3) Let the vertical distance of the second section from the landing to the door be x.

Now, since we know the horizontal distance for this second section as 9 ft and the slope as 1/18, then by proportion, to get the vertical distance (x), we will just multiply the horizontal distance by the slope.

• 4) Since the vertical distance from landing to the door is labelled as x, then from answer 3 above;

x = 9 × (1/18)

x = 1/2 ft

x = 0.5 ft

• 5) Height of landing above the ground = 1.5 ft

Height from the landing to the door = 0.5 ft

Total distance from ground to the door = 1.5 + 0.5 = 2 ft

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