A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place.
A) $24.3 \mathrm {~m}$
B) $25.3 \mathrm {~m}$
C) $22.3 \mathrm {~m}$
D) $21.3 \mathrm {~m}$
E) $23.3 \mathrm {~m}$

Question

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place. ​
A) $24.3 \mathrm {~m}$
B) $25.3 \mathrm {~m}$
C) $22.3 \mathrm {~m}$
D) $21.3 \mathrm {~m}$
E) $23.3 \mathrm {~m}$

Quizplus · Accepted Answer

The conveyor forms a right-angled triangle with the vertical rise as one leg (4 meters) and the horizontal distance as the other leg. The length of the conveyor is the hypotenuse. Using the Pythagorean theorem, $c = \sqrt{a^2 + b^2}$, where $a = 4$ meters (vertical rise), and $b$ can be found from the ratio given (3 meters rise for every 5 meters of horizontal travel). Since the actual rise is 4 meters, we use the ratio to find the actual horizontal distance: $5/3 = b/4$, solving for $b$ gives $b = (5/3) * 4 = 20/3$ meters. Now, $c = \sqrt{4^2 + (20/3)^2} = \sqrt{16 + 400/9} = \sqrt{144 + 400}/3 = \sqrt{544}/3 \approx 23.3$ meters.

A Moving Conveyor Is Built So That It Rises 3 24.3 m24.3 \mathrm {~m}24.3 m

A Moving Conveyor Is Built So That It Rises 3 $24.3 \mathrm {~m}$