## Elementary Algebra

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.