Answer
Machine A works at 60 candies per minute while Machine B works at 40 candies per minute.
Work Step by Step
We call t the time it takes machine B. Thus, we obtain:
$\frac{600}{t-5} = \frac{ 600}{t} + 20 $
We create common denominators and solve for t:
$ \frac{600t}{t(t-5)} = \frac{600(t-5)}{t(t-5)} + \frac{20t(t-5)}{t(t-5)}$
Since the denominators are the same, we cancel them out and solve. (Recall, t cannot be negative.)
$ 0 = -3000 +20t^2 -100t \\ 0=20(t-15)(t+10) \\ t=15$
Thus, we find the rates:
B: $ 600 /15 = 40$
Machine A works 20 candies per minute faster, so it works at 60 candies per minute.
