1 / 13

Solving Motion and Work Problems Using Rational Equations

This guide explores how to solve motion problems using rational equations and the distance formula (d = rt). It includes detailed examples involving relative speeds of cars and a fisherman navigating downstream and upstream, as well as collaborative work scenarios for completing tasks together. Additionally, it covers the concept of ratios and proportions, illustrated with practical examples like salary adjustments based on hours worked and determining heights using similar triangles. Enhance your problem-solving skills with these practical applications.

luka
Download Presentation

Solving Motion and Work Problems Using Rational Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Sections 6.7 Applications Using Rational Equations

  2. Motion Problem The distance formula: d = rtor r = d/tor t = d/r You may want to find the following table helpful in solving motion problem.

  3. Example 1 The top speed of car A is 33 mph less than the top speed of car B. At their top speeds, car B can travel 6 miles in the same time that car A can travel 5 miles. Find the top speed of each car. Let x be the top speed of car A Then (x + 33) is the top speed of car B

  4. Solution The top speed of car A is The top speed of car B is

  5. Example 2 A fisherman travels 9 miles downstream with the current in the same time that he travels 3 miles upstream against the current. If the speed of the current is 6 mph, what is the speed at which the fisherman travels in still water? Let x be the speed at which the fisherman travels in still water. 6mph

  6. Share-Work Problems Rate of work: If a job can be completed in t units of time, then the rate of work is 1/t Similar to the distance formula, we have the following Work completed = rate x time or W = rt

  7. Example 3 Joe can paint a house in 3 hours. Sam can paint the same house in 5 hours. How long does it take them to paint together? Answer: http://www.youtube.com/watch?v=VnOlvFqmWEY

  8. Example 4 The CUT-IT-OUT lawn mowing company consists of two people: Tina and Bill. If Bill cuts a lawn by himself, he can do it in 4 hrs. If Tina cuts the same lawn herself, it takes her an hour longer than Bill. How long would it take if they worked together?

  9. Ratios • The ratio of a to b is or a to b or a:b • A Proportionis a statement that two ratios are equal. In other words, a proportion has the form

  10. Examples Solve the following proportions

  11. Example Billie earns $412 for a 40-hour week. If she missed 10 hours of work last week, how much did she get paid?

  12. Similar Triangles

  13. Example A tree casts a shadow 18 ft long at the same time as a woman 5 feet tall casts a shadow 1.5 feet long. Find the height of the tree.

More Related