Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time, in hours, that machine B must operate?
This is how I solved it. Can you tell me if it is wrong or not?
Maximum hours machines can operate is 8.
So I said 8 * 9000 = 72000
That is 28000 short of 100,000
so 28000/7000 = 4 and hence Machine B only needs to operate 4 hours.
Is this the right way? The answer is 4 but I want to make sure I'm not just getting the right answer by luck.