To determine how long it will take to assemble 125 amplifiers, we need to follow a methodical step-by-step approach:
1. Determine the rate of production per minute:
- We know that it takes 30 minutes to assemble 5 amplifiers.
- Therefore, the rate of production is [tex]\(\frac{5 \text{ amplifiers}}{30 \text{ minutes}}\)[/tex].
- Simplifying this fraction gives us the rate of production per minute.
[tex]\(\frac{5}{30} = \frac{1}{6}\)[/tex] amplifier per minute.
2. Calculate the total time in minutes to produce 125 amplifiers:
- Now that we know the rate is [tex]\(\frac{1}{6}\)[/tex] amplifier per minute, we can find out how many minutes it will take to produce 125 amplifiers by dividing the total number of amplifiers by the rate of production.
- Total time in minutes = [tex]\(\frac{125 \text{ amplifiers}}{\frac{1 \text{ amplifier}}{6 \text{ minutes}}}\)[/tex] = [tex]\(125 \times 6 = 750 \text{ minutes}\)[/tex].
3. Convert the total time from minutes to hours and minutes:
- Since there are 60 minutes in an hour, we can convert 750 minutes to hours and minutes.
- First, divide 750 by 60 to find the number of hours: [tex]\(750 ÷ 60 = 12.5\)[/tex] hours.
- The integer part of the division is the total hours, which is 12 hours.
- The decimal part of the division indicates a fraction of an hour which needs to be converted to minutes.
- [tex]\(0.5\)[/tex] hours is equivalent to [tex]\(0.5 \times 60 = 30\)[/tex] minutes.
Therefore, it will take 12 hours and 30 minutes to assemble 125 amplifiers.
The correct answer is:
B. 12 hours 30 minutes
