Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.1 Number Theory: Prime and Composite Numbers - Exercise Set 5.1: 117

Answer

Two movies will start at the same time again after: $2300$ minutes or $38$ hours and $20$ minutes after.

Work Step by Step

To know when the two movies will start again at the same time after noontime, one must use the least common multiple (LCM). Since there is a 15-minute break between shows, find the LCM of: $85 + 15 = 100$ minutes and $100 +15 = 115$ minutes Factor each number completely : $100 = 10(10) = 2(5) \cdot (2)(5) = 2(2)(5)(5)=2^2\cdot 5^2 \\115 = 5(23)$ Thus, the LCM is $2^2 \cdot 5^2 \cdot 23=2300$ minutes. $2300$ minutes is $38$ hours and $20$ minutes. Thus, the two movies will start at the same time $2300$ minutes or $38$ hours and $20$ minutes after.
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