Using Rational Equations

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Using Rational Equations Sections 6.7 Applications Using Rational Equations

Motion Problem The distance formula: d = rt or r = d/t or t = d/r You may want to find the following table helpful in solving motion problem. Distance Rate/speed Time Quantity 1/Case 1 Quantity 2/ Case 2

Example 1 Let x be the top speed of car A 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

Solution x x + 33 The top speed of car A is The top speed of car B is Distance (miles) Rate/speed (mph) Time (hours) Car A x Car B x + 33

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. Distance (miles) Rate/speed (mph) Time (hours) Downstream x + 6 Upstream x – 6 6mph

Work completed = rate x time 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

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

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?

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

Examples Solve the following proportions

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

Similar Triangles

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.