Explanation Given: One automatic machine can package 100 boxes of machine parts in 12 min, and second machine can do it in 10 min, and a third newer model machine can do it in 8.0 min. Calculation: In order to find the time in which the three machines are working together to complete the job, first set up the equation and then solve it to find the time. Let r 1 , r 2 , and r 3 be the rates of three machines, respectively. Since the first machine can pack 100 boxes of machine pats in 12 min, the rate at which this machine is doing work is r 1 = 100 12 . Similarly, since the second machine can pack 100 boxes of machine pats in 10 min, the rate at which this machine is doing work is r 2 = 100 10 . And since the third newer model machine can pack 100 boxes of machine pats in 8.0 min, the rate at which this machine is doing work is r 3 = 100 8.0 . Let t be the time in minutes to complete the job while the three packaging machines are working together. Hence, the equation that represents the statement “Three machines work together at the rates r 1 , r 2 and r 3 , respectively to package 100 boxes of machine parts by taking t minutes” is r 1 t + r 2 t + r 3 t = 100 . Substitute r 1 = 100 12 , r 2 = 100 10 , and r 2 = 100 8.0 in r 1 t + r 2 t + r 3 t = 100 in order to obtain the required equation. 100 12 × t + 100 10 × t + 100 8.0 × t = 100 100 t 12 + 100 t 10 + 100 t 8.0 = 100 Solve the equation, 100 t 12 + 100 t 10 + 100 t 8.0 = 100 for t as follows. 100 t 12 + 100 t 10 + 100 t 8

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 6.7, Problem 53E

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The time taken by the three machines working together to complete the job.

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Chapter 6.7, Problem 52E

Chapter 6.7, Problem 54E

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Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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