# Lesson33 - Lesson 33, Section 6.5 Application Problems...

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1 Lesson 33, Section 6.5 Application Problems Using Rational Equations 1. Define a Variable 2. Develop A Plan 3. Write an Equation 4. Solve and Answer the Question 1) The reciprocal of 5, plus the reciprocal of 7, is the reciprocal of what number? Let x = the number Reciprocal of 5 plus reciprocal of 7 = reciprocal of x 2) The sum of a number and 21 times its reciprocal is 10 - . Find the number. Let n = the number The number plus 21(reciprocal of number) = 10 -

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2 Job or Work Problems: Suppose Joe can paint a house in 9 hours and Clyde can paint the same house in 12 hours. Examine the table below that shows the fractional part of the job that each man does plus the part of the job that is completed together at that time. TIME Fraction Joe of the house Clyde Painted Together 1 hour 1 9 1 12 1 1 7 or 9 12 36 + 2 hours 2 9 2 1 or 12 6 2 1 7 or 9 6 18 + 3 hours 3 1 or 9 3 3 1 or 12 4 1 1 7 or 3 4 12 + t hours 9 t 12 t 9 12 t t + If the job is to be completed by both together, then 1 9 12 t t + = , where t is time both worked together. This leads to the following summary to model uniform job or work problems.
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Lesson33 - Lesson 33, Section 6.5 Application Problems...

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