Question 365062
karla, pam, and sandy working together can do a job in two hours.
 karla and pam working together can do a job in four hours.
 pam and sandy can do a job in three hours. how long does it take for each
 person to do the job working alone?
:
Write an equation for each statement: Let the completed job = 1
:
"karla, pam, and sandy working together can do a job in two hours."
{{{2/k}}} + {{{2/p}}} + {{{2/s}}} = 1
:
"karla and pam working together can do a job in four hours."
{{{4/k}}} + {{{4/p}}}  = 1
:
"pam and sandy can do a job in three hours."
{{{3/p}}} + {{{3/s}}} = 1
:
This will lend itself easily to elimination, 
multiply the 1st equation by 2, subtract the 2nd equation
{{{4/k}}} + {{{4/p}}} + {{{4/s}}} = 2
{{{4/k}}} + {{{4/p}}} + 0 = 1
----------------------------------subtraction eliminates k and p, find s
{{{4/s}}} = 1
s = 4 hrs
:
Find p, replace s with 4
{{{3/p}}} + {{{3/4}}} = 1
Multiply by 4p
4(3) + 3p = 4p
12 = 4p - 3p
p = 12 hrs
:
Find k, replace p with 12
{{{4/k}}} + {{{4/12}}}  = 1
multiply by 12k
12(4) + 4k = 12k
48 = 12k - 4k
k = {{{48/8}}}
k = 6 hrs
:
Sumarize: k=6 hrs, p=12 hrs, s=4 hrs
:
Check solution in the 1st equation:
{{{2/6}}} + {{{2/12}}} + {{{2/4}}} = 
{{{4/12}}} + {{{2/12}}} + {{{6/12}}} = 1; confirms our solutions
:
:
how long does it take karla and sandy working together to do the job?
let t = time for this to be true
{{{t/6}}} + {{{t/4}}} = 1
multiply by 12
2t + 3t = 12
5t = 12
 t = {{{12/5}}}
t = 2.4 hrs, K and S working together