Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 7 - Algebraic Fractions - 7.6 - More Fractional Equations and Problem Solving - Problem Set 7.6: 49

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.
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