# A 14-inch-wide conveyor unloads 2000 bushels of wheat per hour. At this speed, how many bushels...

## Question:

A 14-inch-wide conveyor unloads 2000 bushels of wheat per hour. At this speed, how many bushels per hour will an 21-inch-wide conveyor unload?

## Using Proportionality to Calculate Wheat Bushel Production

Assuming the wheat bushel production per hour is proportional to the width of the conveyor belt that unloads it, we use the given information to find the constant of proportionality. Once we have the constant of proportionality we can use it to find the wheat bushel production from a conveyor belt of much larger width. The concepts used include solving a linear equation from Algebra.

Let w be the width of the conveyor belt and n be the number of bushels of wheat per hour the conveyor belt unloads. Then since n is proportional to w we have a constant k such that

{eq}n = k w \qquad (1) {/eq}

From the information given in the question, when w = 14 inches then n = 2000 bushels per hour. Substituting these values in (1) gives us

{eq}\displaystyle 2000 = k (14) \implies k = \frac {2000}{14} \qquad (2) {/eq}

Using this value of k back in (1) gives us our exact equation as

{eq}\displaystyle n = \frac {2000}{14} w \qquad (3) {/eq}

To find the number of bushels of wheat per hour that a 21-inch-wide conveyor belt can unload we use w = 21 in (3) to get

{eq}\displaystyle n = \frac {2000}{14} (21) = 3000. {/eq}

The 21-inch-wide conveyor belt will unload 3000 bushels of wheat per hour.