Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Review - Exercises - Page 135: 85

Answer

time = 110 minutes = 1 hour and 50 minutes

Work Step by Step

$$v_{Abbie} = 2v_{Beth} = 3v_{Cathie}$$ If $v_{Cathie} = v$, then: $v_{Beth} = \frac 32 v$ $v_{Abbie} = 3v$ y = Total painting area. When they work together, all their speeds are put together: $$(v_{Cathie} + v_{Beth} + v_{Abbie}) \times (time) = y$$ $$(v + \frac 32v + 3v)60 = y$$ $$(2v + 3v + 6v)30 = y$$ $$(11v)30 = y$$ $$330v = y$$ Calculate the time if Abbie worked alone: $$(v_{Abbie} ) \times (time) = y$$ $$3v \times (time) = 330v$$ $$time = \frac{330 v}{3v} = 110v$$ Thus, time = 110 minutes = 1 hour and 50 minutes.
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.