Answer:
To find the rate at which the machine makes nails, you can use the formula:
\[ \text{Rate} = \frac{\text{Amount of Output}}{\text{Time}} \]
In this case, the machine makes \(2 \frac{1}{4}\) kg of nails in \(1 \frac{1}{2}\) hours.
\[ \text{Rate} = \frac{2 \frac{1}{4}\, \text{kg}}{1 \frac{1}{2}\, \text{hours}} \]
First, convert the mixed numbers to improper fractions:
\[ \text{Rate} = \frac{\frac{9}{4}\, \text{kg}}{\frac{3}{2}\, \text{hours}} \]
Now, invert and multiply to find the rate:
\[ \text{Rate} = \frac{\frac{9}{4}\, \text{kg}}{\frac{3}{2}\, \text{hours}} \times \frac{2}{3} \]
Simplify:
\[ \text{Rate} = \frac{\frac{3}{2}\, \text{kg}}{1\, \text{hour}} \]
Therefore, the machine makes nails at a rate of \( \frac{3}{2} \) kg per hour.
