Problem 8

Explanation

We can solve this problem using direct proportion.

Given:

• Capacity of tool A = $3 \times$ capacity of tool B.
• Production of tool B in $5$ hours = $30$ units.

Steps:

1. Calculate the production of tool A in the same time period ($5$ hours). Since A's capacity is $3$ times B's, in $5$ hours:

   $$A_{5\text{hours}} = 3 \times 30 = 90 \text{ units}$$

2. Calculate the production of tool A in $2$ hours. Use the time ratio:

   $$A_{2\text{hours}} = \frac{2}{5} \times 90$$

   $$A_{2\text{hours}} = 2 \times 18$$

   $$A_{2\text{hours}} = 36 \text{ units}$$

Thus, in $2$ hours, tool A can produce $36$ units.