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

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?
...
(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
..
John = x+6 hours
so he does 1/(x+6)of the job in 1 hour
..
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
...
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.
...
m.ananth@hotmail.ca
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