SOLUTION: working together , two people can cut a large lawn in 5 hours. One person can do the job alone in 2 hours les than the other. how long would it take the fastest person to do the jo

Question 388532: working together , two people can cut a large lawn in 5 hours. One person can do the job alone in 2 hours les than the other. how long would it take the fastest person to do the job?
Found 2 solutions by lwsshak3, mananth:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
let x = the number of hours the faster person can do the job alone
x+2 = the number of hours the slower person can do the job alone
rate of faster person = 1/x
rate of slower person = 1/(x+2)
rate when both working together = 1/5
1/x +1/(x+2) = 1/5
(x+2+x)/x(x+2)=1/5
(2x+2)/(x^2+2x)=1/5
10x8x+10=(x^2+2x)
x^2-8x-10=0
solve by completing the square(alternatively use quadradic formula)
(x^2-8x+16)-16-10=0
(x-4)^2=26
x-4=sqr root of 26
x=4+sqr root of 26(reject negative root)
Ans: the faster person can do the job alone in about 9.1 hours
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
working together , two people can cut a large lawn in 5 hours. One person can do the job alone in 2 hours les than the other. how long would it take the fastest person to do the job?
...
Two people 5 hours
1/5 of job they do in 1 hour.
...
let one of them take x hours
so he does 1/x of the job in 1 hour.
..
the other takes 2 hours less than the first = x-2 hours.
so he can do 1/(x-2) of the job in 1 hour.
..
1/x + 1/(x-2)= 1/5
LCD = x(x-2)
multiply by x(x-2)
(x-2+x)/x(x-2)=1/5
2(x-1)/x(x-2)=1/5
cross multiply
10(x-1)=x(x-2)
10x-10=x^2-2x
x^2-12x+10
solve using quadratic formula
b^2-4ac= 104

x1= 11.09 hours
the faster person will take 9.09 hours to do the job alone
...
m.ananth@hotmail.ca
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