Question

A new banquet hall has ordered carpeting from a factory from a factory for their new room. The carpet factory can produce 1 square yard of carpet every 10 min. How many hours would it take the factory to produce 25 1/2 square yards of carpet for the banquet hall? Plzzzz write a proportion I will give you 100 points

Answer 1

A proportion says: (one fraction) is equal to (another fraction)

or (one ratio) is equal to (another ratio).

In this question, the ratio is (the area of a piece of carpet) to (the time it takes to manufacture it.

And we know we can write the ratio as (1 square yard) / (10 minutes).

The other ratio is (25.5 square yards) / (how long THOSE take).

The carpet factory works at a constant rate, so we know that those two ratios are equal. So we can write:

(1 yd²) / (10 min) = (25.5 yd²) / (how long that piece takes) .

To solve a proportion, you "cross multiply". That means

(left top) x (right bottom) = (left bottom) x (right top)

(1 yd²) x (how long the big piece takes) = (25.5 yd²) x (10 min)

There's an equation to solve.

Divide each side by (yd²):

(how long the big piece takes) = (25.5) x (10 min)

How long the big piece takes = 255 minutes

BUT ... the question wants to know "How many hours ..." , so you have to convert the 255 minutes into hours. You should be able to do that, because you certainly know that 60 minutes = 1 hour.

Big piece = (255 minutes) x (1 hour / 60 minutes)

Big piece = (255/60) hours

Big piece = 4.25 hours (that's 4 hours 15 minutes)