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: 98

Answer

360 seconds, which is equal to 6 minutes.

Work Step by Step

To find when the two bikers will be back at the starting point together, we need to find the Least Common Multiple of 40 and 45 (Their times around the track, in seconds). To do this, we need to prime factor the numbers. 40 = 2 x 2 x 2 x 5 45 = 3 x 3 x 5 The LCM has to have every possible number from the prime factors: it has the 2 x 2 x 2 x 5 from the 40. Since the 45's prime factors are 3 x 3 x 5, and we already have a five from the 40, we only need to include 3 x 3 from the 45. Therefore, the LCM of 40 and 45 is 2 x 2 x 2 x 5 x 3 x 3 = 360 seconds. 360 seconds is equal to 6 minutes.
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