## Thinking Mathematically (6th Edition)

Published by Pearson

# 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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