The "12,000 rivets" is just a distraction -- we can call it "one job". To work out how quickly the machines work together, we can get the same time for the two types of machine; since we have x hours and 3x hours, using 3x hours is convenient:
A does 3 jobs in 3x hours
B does 1 job in 3x hours
A+B together do 4 jobs in 3x hours
A+B together do 1 job in 3x/4 hours
That's using 1 of each type of machine. If we instead use n machines of each type, we'll divide the total time taken by n. We want this total time to be less than x/9, so we have
3x/4n < x/9
27 < 4n
27/4 < n
n needs to be an integer, so n needs to be at least 7, and since we're using 7 of each type of machine, we'll need at least 14 machines in total.
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