## Elementary Algebra

We call t the time it takes the Tchaika. Thus, we obtain: $\frac{300}{t-10} = \frac{ 300}{t} - 5$ We create common denominators and solve for t: $\frac{300t}{t(t-10)} = \frac{300(t-10)}{t(t-10)} + \frac{5t(t-10)}{t(t-10)}$ Since the denominators are the same, we cancel them out and solve. (Recall, t cannot be negative.) $0 = -3000 + 5t^2 -50t \\ 5(t-30)(t+20)$ Since t cannot be negative, we see that t equals 30. Thus, we find the rates: Tchaika: $300/30 =10$ The Pachena are 5 oysters per minute faster, so they work at a rate of 15.