Final answer:
It would take 8 minutes for just 1 machine to produce a batch, and it would take 64 minutes for 8 machines to produce a batch.
Step-by-step explanation:
a) To find how many minutes it would take just 1 machine, we can set up a proportion. Since it takes 48 minutes for 6 machines to produce a batch, we can set it up like this:
6 machines / 48 minutes = 1 machine / x minutes
Cross-multiplying, we get: 6x = 48
Dividing both sides by 6, we find that x = 8
Therefore, it would take 8 minutes for just 1 machine to produce a batch.
b) To find how many minutes it would take 8 machines, we can use the same proportion:
6 machines / 48 minutes = 8 machines / x minutes
Cross-multiplying, we get: 6x = 48 * 8
Dividing both sides by 6, we find that x = 64
Therefore, it would take 64 minutes for 8 machines to produce a batch.