Question

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 1/18 and covers another 9 feet of horizontal distance to reach the door.

a) 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.

b) 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 steeper.

c) 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)?

d) What is the vertical distance (rise) from the landing to the door? Show your work.

e) What is the total height of the door above the ground?

Answer 1

a) The slope of the ramp from the ground to the landing is 1.5/18. b) The steeper part of the ramp is from the ground to the landing. c) To find the vertical distance (rise), multiply the run by the slope.

Step-by-step explanation:

a) The slope of the ramp from the ground to the landing can be found by dividing the vertical distance (rise) by the horizontal distance (run). The rise is 1.5 feet and the run is 18 feet. Therefore, the slope is 1.5/18.

b) To determine which part of the ramp is steeper, we compare the slopes. The slope from the ground to the landing is 1.5/18, while the slope from the landing to the door is 1/18. Since 1/18 is a smaller fraction than 1.5/18, the steeper part is from the ground to the landing.

c) If you know the horizontal distance (run) and the slope, you can find the vertical distance (rise) by multiplying the run by the slope. For example, if the run is 9 feet and the slope is 1/18, the rise is 9 * (1/18) = 0.5 feet.

d) The vertical distance (rise) from the landing to the door can be found using the same method as in part c. The run is 9 feet and the slope is 1/18, so the rise is 9 * (1/18) = 0.5 feet.

e) The total height of the door above the ground is the sum of the rise from the ground to the landing (1.5 feet) and the rise from the landing to the door (0.5 feet). Therefore, the total height is 1.5 + 0.5 = 2 feet.