Question 388532
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