Question

the production line where you work can assemble 5 amplifiers every 30 minutes. at this rate, how long should it take the line to assemble 125 amplifiers?
a. 4 hours 10 minutes
b. 12 hours 30 minutes
c. 12 hours 50 minutes
d. 20 hours 50 minutes
e. 25 hours

Explanation:

Step1: Find rate per amplifier

First, convert 30 minutes to hours: \( 30 \text{ minutes} = \frac{30}{60} = 0.5 \text{ hours} \).
The production line assembles 5 amplifiers in 0.5 hours. So the time per amplifier is \( \frac{0.5 \text{ hours}}{5} = 0.1 \text{ hours per amplifier} \).

Step2: Calculate time for 125 amplifiers

Multiply the time per amplifier by 125: \( 0.1 \times 125 = 12.5 \text{ hours} \).
Convert 0.5 hours to minutes: \( 0.5 \times 60 = 30 \text{ minutes} \).
So total time is 12 hours 30 minutes? Wait, no—wait, wait, let's recheck. Wait, 5 amplifiers in 30 minutes. So rate is 5 amplifiers / 30 minutes = 1 amplifier / 6 minutes. So time for 125 amplifiers: \( 125 \times 6 = 750 \text{ minutes} \). Convert 750 minutes to hours: \( 750 \div 60 = 12.5 \) hours, which is 12 hours 30 minutes? Wait, but wait, the options: Wait, maybe I misread the problem. Wait, the problem says "assemble 5 amplifiers every 30 minutes". So time to assemble 125 amplifiers. Let's do it with minutes. 30 minutes for 5 amplifiers. So for 125 amplifiers, how many 5 - amplifier sets? \( 125 \div 5 = 25 \) sets. Each set takes 30 minutes, so total minutes: \( 25 \times 30 = 750 \) minutes. Convert to hours: \( 750 \div 60 = 12.5 \) hours, which is 12 hours 30 minutes. Wait, but option B is 12 hours 30 minutes? Wait, but let's check the options again. Wait, the options are: A. 4h10m, B.12h30m, C.12h50m, D.20h50m, E.25h. Wait, but 125 amplifiers: 5 per 30 minutes. So 125 /5 =25. 2530=750 minutes. 750/60=12.5 hours=12h30m. So option B? Wait, but maybe I made a mistake. Wait, no—wait, 5 amplifiers in 30 minutes. So time per amplifier: 30/5=6 minutes per amplifier. 1256=750 minutes. 750/60=12.5 hours=12h30m. So the answer should be B.

Wait, but wait, the original problem's options: Let me check again. The options are:

A. 4 hours 10 minutes

B. 12 hours 30 minutes

C. 12 hours 50 minutes

D. 20 hours 50 minutes

E. 25 hours

Yes, so the correct calculation gives 12 hours 30 minutes, which is option B.

Answer:

B. 12 hours 30 minutes