If five machines take 5 minutes to make five gadgets, how long would it take 100 machines to make 100 gadgets?
The correct answer and explanation is:
Correct Answer: 5 minutes
To understand the problem, we must recognize that the key lies in the relationship between the number of machines, the time taken, and the number of gadgets produced.
The question states that five machines take 5 minutes to make five gadgets. This means that each machine takes 5 minutes to make one gadget. All machines are working at the same time, in parallel.
So, in 5 minutes:
- One machine makes one gadget
- Five machines make five gadgets
- The production rate is 1 gadget per machine every 5 minutes
Now, if there are 100 machines, and each machine still makes 1 gadget in 5 minutes, then in 5 minutes:
- 100 machines will each produce 1 gadget
- Therefore, 100 machines produce 100 gadgets in 5 minutes
It is important to note that increasing the number of machines does not increase the time; it increases the output during the same time period, because they all work simultaneously.
This is an example of a constant rate of production per machine, with output scaling linearly with the number of machines. The total time required to make a certain number of gadgets depends not on the number of gadgets alone, but on how many machines are available to make them at once. Since the number of machines matches the number of gadgets and each machine takes 5 minutes to make one gadget, the entire job is completed in 5 minutes.
This problem often confuses people because they mistakenly apply sequential logic instead of parallel logic. The machines are not working one after the other; they are working at the same time. Therefore, 100 machines can make 100 gadgets in just 5 minutes.