Uniform rates exercises in practical applications

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SUMMARY

The discussion centers on the practicality of uniform rates problems beyond traditional applications such as inlet and outlet pipes for reservoirs. Participants express skepticism regarding the relevance of these problems in real-world scenarios, noting that while they yield rational equations, many examples appear artificial and serve primarily as academic exercises. However, the conversation highlights that uniform rates concepts are applicable in everyday decision-making, such as comparing costs of different quantities of products. The need for more diverse examples in Intermediate Algebra textbooks is emphasized.

PREREQUISITES
  • Understanding of uniform rates problems in mathematics
  • Familiarity with rational equations
  • Basic knowledge of direct proportionality in physics
  • Intermediate Algebra concepts
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  • Research practical applications of uniform rates in economics
  • Explore real-world examples of rational equations in engineering
  • Investigate the use of uniform rates in project management scenarios
  • Learn about direct proportionality and its applications in various scientific fields
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Students and educators in mathematics, particularly those teaching or learning Intermediate Algebra, as well as professionals in fields such as engineering, economics, and project management who seek to apply mathematical concepts to real-world situations.

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Are the simple uniform rates problems practical for anything other than for applications like inlet and outlet pipes filling or draining a reservoir? The kind I mean are the ones which immediately yield rational equations immediately upon first analysis. We find motion problems, we find job-work rate problems about people and copy machines, but many of these seem impractical, appearing to be just unnecessary ways to create exercises. The only kind of uniform rates problems which seem useful are the pipes filling or draining reservoirs. If anyone knows of applications which are not typically shown in Intermediate Algebra textbooks but are still at this level, telling about them would be very interesting.
 
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Yes, those problems posed in exercises are usually very artificial. But we solve these kind of problems at their basic level all the time if we e.g. decide whether a the big box of something is cheaper than the small box, or what a few of something cost, given the price of one.

In physics we have many direct proportional quantities:
##F \sim a\, , \,U \sim R\, , \,W \sim h\, , \,C \sim Q## etc.
 

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