SOLUTION: together it takes john and carl 6hours and 25 minutes to sort recycyle material. Alone, John would require 6 more hours than carl. how long would it take carl to do the job alone
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Question 384360: together it takes john and carl 6hours and 25 minutes to sort recycyle material. Alone, John would require 6 more hours than carl. how long would it take carl to do the job alone?
(x+6) John
x carl
385 is 6 hours & 25 min converted to minutes
1/(x+6) + 1/x = 385
LCD is 385x(x+6)
385x +385x + 2310=385x^2+2310x
770x+2310=385x^2+2310x
how do i foil or what next???
=385x^2-1540x-2310 Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! together it takes john and carl 6hours and 25 minutes to sort recycyle material. Alone, John would require 6 more hours than carl. how long would it take carl to do the job alone?
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(Please note either you do the working in minutes or hours. not both)I have converted 6 hours 25 minutes to hours 6 5/12= 77/12
carl x hours
so he does 1/x of the job in 1 hour
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John = x+6 hours
so he does 1/(x+6)of the job in 1 hour
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together they will do 1/x + 1/(x+6) job in 1 hour
=x+6+x/(x(x+6))
=(2x+6)/(x^2+6x) of the job in 1 hour
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they will take (x^2+6x) /(2x+6) hours together to do the job
cross multiply
12(x^2+6x)=77(2x+6)
12x^2+72x=154x+462
12x^2+72x-154x-462=
12x^2-82x-462=0
/2
6x^2-41x-231=0
solve for x using quadratic formula
discriminant =7225
x1=10.50 hours
Carl takes 10.50 hours to complete the job alone
x2 will be negative so ignored.
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m.ananth@hotmail.ca
