SOLUTION: Jack, Kay, and Lynn deliver flyers. If alone Jack takes 4 hours, and Lynn takes 1 hour longer than Kay. Together they can deliver in 40% of the time it takes Kay working alone. *

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jack, Kay, and Lynn deliver flyers. If alone Jack takes 4 hours, and Lynn takes 1 hour longer than Kay. Together they can deliver in 40% of the time it takes Kay working alone. *      Log On


   

Question 178527This question is from textbook Precalculus
: Jack, Kay, and Lynn deliver flyers. If alone Jack takes 4 hours, and Lynn takes 1 hour longer than Kay. Together they can deliver in 40% of the time it takes Kay working alone. *How long does it take Kay to deliver all the flyers alone?* This question is from textbook Precalculus

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
Jack can do 1/4 of the job per hour. Lets call the time it takes kay k and therefore Lynns time to do the job will be k+1
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so Kay can do 1/k of the job per hour
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and Lynn can do 1/(k+1) per hour
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%28%281%2F4%29%2B%281%2Fk%29%2B1%2F%28k%2B1%29%29%28.4k%29=1%28job%29
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common denominator is 4k(k+1)
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%28%28k%28k%2B1%29%2B4k%2B4%28k%2B1%29%29%2F4k%28k%2B1%29%29%28.4k%29=1
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%28%28k%28k%2B1%29%2B4k%2B4%28k%2B1%29%29%2Fk%28k%2B1%29%29%28.4%29=1k's cancelled on left side
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k%28k%2B1%29%2B4k%2B4%28k%2B1%29=4%28k%2B1%29%2F%28.4%29.....multiplied both sides by 4(k+1)and divided by .4
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k%5E2%2Bk%2B4k%2B4k%2B4=10k%2B10distributed and carried out operations
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k%5E2%2B9k%2B4=1k%2B10combined like terms on each side
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k%5E2-k-6=0....collected terms on one side
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%28k-3%29%28k%2B2%29=0factored
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k=3 and -2...throw out the negative value
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highlight%28k=3%29hours.