Question 309458
a, b, and c can finish a job in 6 days.
 if b and c work together, the job will take 9 days;
if a and c work together, the job will be done in 8 days. 
in how many days can each man working alone do the job?
:
Let the completed job = 1
:
"a, b, and c can finish a job in 6 days."
1.{{{6/a}}} + {{{6/b}}} + {{{6/c}}} = 1
:
"if b and c work together, the job will take 9 days;"
2.{{{9/b}}} + {{{9/c}}} = 1
:
"if a and c work together, the job will be done in 8 days."
3.{{{8/a}}} + {{{8/c}}} = 1
:
Multiply eq1 by 3, and eq2 by 2
{{{18/a}}} + {{{18/b}}} + {{{18/c}}} = 3
{{{0/a}}} + {{{18/b}}} + {{{18/c}}} = 2
--------------------------subtraction eliminates a & b, find c
18/a = 1
Mult both sides by a
a = 18 hrs alone
:
replace a with 18 in eq3, find c
{{{8/18}}} + {{{8/c}}} = 1
Multiply by 18c
8c + 18(8) = 18c
8c + 144 = 18c
144 = 18c - 8c
144 = 10c
c = {{{144/10}}}
c = 14.4 hrs alone
:
replace c with 14.4 in eq2, find b
{{{9/b}}} + {{{9/14.4}}} = 1
multiply by 14.4b
14.4(9) + 9b = 14.4b
129.6 = 14.4b - 9b
129.6 = 5.4b
b = {{{129.6/5.4}}}
b = 24 hrs alone
:
solution: a=18 hrs, b=24 hrs, c= 14.4 hrs
:
See if that flies in the eq1
{{{6/18}}} + {{{6/24}}} + {{{6/14.4}}} 
.333 + .25 + .417 = 1