Answer
The Tchaika works at 10 oysters per minute, and the Pachena works at 15 oysters per minute.
Work Step by Step
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.
