Explanation Given information: It is provided that I was one tenth of a mile from the intersection and aunt was one tenth of twentieth of a mile from it where aunt and I were approaching the same intersection point, aunt started from the south with a steady speed of 10 mph towards the intersection and I started from west with a speed of 60 mph towards the intersection. Formula used: The steps for solving the related rate problem are: Step1: List the changing and related quantities followed by restating the problem in rate of change of terms. Step 2: Rewrite the problem using for the changing quantities for their derivatives. Step 3: If possible draw the diagram of the changing quantities and find an equation relating the changing quantities. Step 4: Differentiate with respect to the equation (s) in order to get rate of change in relating quantity. Step 5: Now substitute the values of the provided quantity and their derivative into the derived equation and solve them to get answer. The Pythagorean Theorem: In a right angle triangle with base of length b , height of length h and the hypotenuse of length c , the sum of the square of base length and the square of height length is equals to the length of hypotenuse. b 2 + h 2 = c 2 Calculation: Let x be the distance of the aunt from the intersection, y be the distance of myself from the intersection and z be the distance between them. Consider the steps of the formula: The changing quantities are x , y , z as described above. Since, I was one tenth of a mile from the intersection and started from west with a speed of 60 mph towards the intersection. Thus, the rate of change of y is 60 and y = 1 10 . Thus, d y d t = 60 when y = 1 10 Since, aunt was one tenth of twentieth of a mile from it and she started from the south with a steady speed of 10 mph towards the intersection. Thus, the rate of change of x is 10 and the value of x is 1 20 . Thus, d x d t = 10 when x = 1 20 Since, the rate at which they were approaching each other is to be determined. What is the rate of change of z ? d z d t = ? Since, they approach to a common intersection point and the distance of them from the intersection point forms the right angle, thus it forms a right angle triangle with height y , base x and the hypotenuse z . Thus, consider the Pythagorean theorem

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 12.5, Problem 34E

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To calculate: The rate at which they were approaching each other at the instant when I was one tenth of a mile from the intersection and aunt was one tenth of twentieth of a mile from it where aunt and I were approaching the same intersection point, aunt started from the south with a steady speed of 10 mph towards the intersection and I started from west with a speed of 60 mph towards the intersection.

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Chapter 12.5, Problem 33E

Chapter 12.5, Problem 35E

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Solution Summary: The author calculates the rate at which aunt and aunt were approaching each other at the instant when they were one tenth of a mile away.

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