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Below is a transcription of a (fictional) student's solution to a related rates problem. There are several flaws in the solution: at least three procedural errors, and room for improvement in the presentation. For each flaw that you find, say what the mistake is, and how to fix it. Problem: Two cars leave from an intersection at the same time. Car A travels south at 80 km/h, while car B travels east at 60 km/h. At what rate is the distance between the cars increasing one hour later?

Below is a transcription of a (fictional) student's solution to a related rates problem. There are several flaws in the solution: at least three procedural errors, and room for improvement in the presentation. For each flaw that you find, say what the mistake is, and how to fix it. Problem: Two cars leave from an intersection at the same time. Car A travels south at 80 km/h, while car B travels east at 60 km/h. At what rate is the distance between the cars increasing one hour later?

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter14: Sequences And Mathematical Induction
Section14.3: Another Look At Problem Solving
Problem 29PS
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Below is a transcription of a (fictional) student's solution to a related rates problem. There are several flaws in the solution: at least three procedural errors, and room for improvement in the presentation. For each flaw that you find, say what the mistake is, and how to fix it. Problem Two cars leave from an intersection at the same time Car A travels south at 80 km/h, while car B travels east at 60 km/h. At what rate is the distance between the cars increasing one hour later?
Transcribed Image Text:Below is a transcription of a (fictional) student's solution to a related rates problem. There are several flaws in the solution: at least three procedural errors, and room for improvement in the presentation. For each flaw that you find, say what the mistake is, and how to fix it. Problem Two cars leave from an intersection at the same time Car A travels south at 80 km/h, while car B travels east at 60 km/h. At what rate is the distance between the cars increasing one hour later?
Solution (my beautiful ASCII triangle diagram isn't one of the flaws) 一 y / 1 7 From the diagram, x2 +y2 = z² So da dy +y' dt dz 2. 2. dt dt dy Car A is travelling south, and that's negative, so dt 60. Car B is travelling east, and that's positive, so = 80 dr dt After one hour, car A has gone 60 km and car B has gone 80 km, and /(60)? + (80)² = 60 + 80 = 140 Plugging in: dz 60 (-60) + 80° (80) = 1402 dt dz 296000 15.1km/h dt 19600
Transcribed Image Text:Solution (my beautiful ASCII triangle diagram isn't one of the flaws) 一 y / 1 7 From the diagram, x2 +y2 = z² So da dy +y' dt dz 2. 2. dt dt dy Car A is travelling south, and that's negative, so dt 60. Car B is travelling east, and that's positive, so = 80 dr dt After one hour, car A has gone 60 km and car B has gone 80 km, and /(60)? + (80)² = 60 + 80 = 140 Plugging in: dz 60 (-60) + 80° (80) = 1402 dt dz 296000 15.1km/h dt 19600
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