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: 50


Machine A works at 60 candies per minute while Machine B works at 40 candies per minute.

Work Step by Step

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.
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