moving conveyor is built to rise 1 meter for every 5 meters of horizontal change. Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor if the Vertical distance between floors is 10 meters. Round your answer to the nearest meter.
A)61 meters
B)39 meters
C)51 meters
D)50 meters
E)41 meters

Question

Quizplus · Accepted Answer

Since the conveyor rises 1 meter for every 5 meters of horizontal change, we can set up a proportion:
Vertical distance/horizontal distance = 1/5
Plugging in the given vertical distance of 10 meters:
10/horizontal distance = 1/5
Solve for the horizontal distance:
horizontal distance = 50 meters
Add the horizontal distance to the initial and final vertical distances:
50 + 10 + 10 = 70 meters
However, since the question asks for the length of the conveyor, we need to account for the diagonal length:
Using the Pythagorean theorem, where c is the length of the conveyor:
a^2 + b^2 = c^2
10^2 + 50^2 = c^2
2500 = c^2
c ≈ 50.0 meters
Rounded to the nearest meter, the answer is therefore 51 meters (Choice C).

Moving Conveyor Is Built to Rise 1 Meter for Every