Question

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

• A. 10800
• B. 648
• C. 1800
• D. 2700

Hint:

In work-rate problems, always find the unit rate first (e.g., work done by one person/machine in one unit of time). Once you have the unit rate, you can easily scale it up for any number of workers and any amount of time.

Answer 1

The Correct Option is C

This is a rate problem that can be solved in steps.

Step 1: Find the rate of a single machine. 6 machines produce 270 bottles per minute.
Rate of 1 machine = \( \frac{\text{Total production}}{\text{Number of machines}} = \frac{270 \text{ bottles/min}}{6 \text{ machines}} = 45 \) bottles per minute per machine.

Step 2: Find the combined rate of 10 machines. Combined rate = Rate of 1 machine \( \times \) Number of machines Combined rate = \( 45 \text{ bottles/min/machine} \times 10 \text{ machines} = 450 \) bottles per minute.

Step 3: Calculate the total production in 4 minutes. Total production = Combined rate \( \times \) Time Total production = \( 450 \text{ bottles/min} \times 4 \text{ min} = 1800 \) bottles.
So, 10 machines can produce 1800 bottles in 4 minutes.