Explanation Given: The time taken for the first leg is d v 1 . The time taken for the second leg is d v 2 . The total distance traveled is 2 d . Procedure used: Addition or Subtraction of Rational Numbers (Fraction) with unlike denominators: 1. Compute the LCD of the denominators. 2. Write fraction with the LCD as the denominator. 3. Add or subtract the numerators and write the result over the common denominator. 4. Write the result in lowest terms. “ Finding the lowest common denominator ( LCD ) : 1. Find the prime factors of each denominator. 2. For each different prime factor that appears, note the highest power to which it is raised in any one of the denominators. 3. Form the product of all the different prime factors, each raised to the power found in step 2. This product is called the lowest common denominator.” Calculation: The expression for the average speed of the round trip is written by dividing the total distance by the sum of the time taken for the first and second leg. That is, 2 d d v 1 + d v 2 . Consider the denominator of the given expression d v 1 + d v 2 . To make the denominators of the fractions equivalent, find the LCD of the denominators. The factor of v 1 is v 1 and the factor of v 2 is v 2 . Therefore, v 1 and v 2 are the factors of the LCD. Thus, the LCD of the denominators of each fractions is the product of v 1 and v 2 that is v 1 v 2 . To make the resulting denominator in each fraction equal to the LCD, multiply and divide the fraction by the proper quantity. d v 1 + d v 2 = d v 1 ⋅ 1 + d v 2 ⋅ 1 = d v 1 ⋅ v 2 v 2 + d v 2 ⋅ v 1 v 1 = d v 2 v 1 v 2 + d v 1 v 2 v 1 = d v 2 v 1 v 2 + d v 1 v 1 v 2 Since the denominators of the fractions are same, add the numerators and keep the denominator as it is

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 6.6, Problem 72E

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To write: The expression for the average speed of the round trip and simplify it.

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Chapter 6.6, Problem 71E

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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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