Question

a factory produces 126 units in \\(\frac{9}{4}\\) hours. how many units does the factory produce per hour?

Explanation:

Step1: Recall the formula for rate

The rate (units per hour) is calculated by dividing the total number of units produced by the total time taken. So, the formula is \( \text{Rate} = \frac{\text{Total Units}}{\text{Total Time}} \).

Step2: Substitute the given values

We know that the total units produced are \( 126 \) and the total time is \( \frac{9}{4} \) hours. So, we substitute these values into the formula: \( \text{Rate} = \frac{126}{\frac{9}{4}} \).

Step3: Simplify the division of fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So, \( \frac{126}{\frac{9}{4}} = 126\times\frac{4}{9} \).

Step4: Calculate the product

First, simplify \( 126\div9 = 14 \). Then, multiply \( 14\times4 = 56 \).

Answer:

The factory produces \( 56 \) units per hour.