Question

Running at the same constant rate, 6 identical machines can produce a total of 180 bottles per hour. How many bottles could 15 such machines produce in 30 minutes?

• A. 225
• B. 300
• C. 250
• D. 350

Hint:

Find bottles per machine per hour, scale to 15 machines, then halve for 30 minutes.

Answer 1

The Correct Option is A

This can also be solved using direct proportion (unitary method) without first finding the single-machine rate explicitly.

1. Bottles produced are directly proportional to both the number of machines and the time worked.
2. Given: 6 machines produce 180 bottles in 60 minutes.
3. Find bottles produced by 1 machine in 1 minute: $\frac{180}{6 \times 60} = \frac{180}{360} = 0.5$ bottles per machine per minute.
4. For 15 machines running for 30 minutes, total bottles $= 15 \times 30 \times 0.5$.
5. Compute: $15 \times 30 = 450$, and $450 \times 0.5 = 225$.
6. So 15 machines produce 225 bottles in 30 minutes, confirming option (1).

\[\boxed{225 \text{ bottles}}\]