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 - Page 315: 49


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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.