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Work problems Mr. Dodson can paint his house by himself in 4 days. His son needs two additional days to complete the job if he works by himself. Find how long it takes to paint the house if they work together. The answer is not 5 hours (no averaging!) The answer is not 10 hours (Makes no sense!!)

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**Solution: x = (2.4 days) [Highlight to reveal]**

Make a chart! Equation set-up: Solution: x = (2.4 days) [Highlight to reveal] Hours to complete total job Part of job completed in 1 hr Mr. Dodson Son Team effort

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Section 5.6: Proportion The directions for a certain bug spray concentrate is to mix 3 ounces of concentrate with 2 gallons of water. How many ounces of water are needed to mix with 9 gallons of water? Set-up: Solution: (13.5 ounces of water are needed) [Highlight to reveal]

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**Sect 5.6: Distance = rate X time**

The current on a portion of the Mississippi River is 3 miles per hour. A barge can go 6 miles upstream in the same amount of time it takes to go 10 miles downstream. Find the speed of the boat in still water (Hint: Let x be the speed of the boat in still water)

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**The current on a portion of the Mississippi River is 3 miles per hour**

The current on a portion of the Mississippi River is 3 miles per hour. A barge can go 6 miles upstream in the same amount of time it takes to go 10 miles downstream. Find the speed of the boat in still water (Let x = boat speed). Need to relate the times! Distance Rate (boat & river) Time Upstream (against river current – slows you down) (Same time) Downstream (with river current – speeds you up) Set-up: Solution: The speed of the boat is (12 miles/hr)

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**Section 5.6: Finding individual time if you know total time**

One custodian cleans a suite of offices in 6 hours. When a second worker is asked to join, the total time to complete the job now takes 1.5 hours. How long does it take the second worker to complete the job working alone?

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**Solution: x = (2 hours) [Highlight to reveal]**

Make a chart! Equation set-up: Solution: x = (2 hours) [Highlight to reveal] Hours to complete total job Part of job completed in 1 hr First worker Second worker Team effort 1.5 or 3/2 1/1.5 = 1/(3/2) = 2/3

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Proportions and Problem Solving with Rational Equations

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