SOLUTION: 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 doe

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? how long does it take karla and sandy working together to do the job?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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."
+ + = 1
:
"karla and pam working together can do a job in four hours."
+ = 1
:
"pam and sandy can do a job in three hours."
+ = 1
:
This will lend itself easily to elimination,
multiply the 1st equation by 2, subtract the 2nd equation
+ + = 2
+ + 0 = 1
----------------------------------subtraction eliminates k and p, find s
= 1
s = 4 hrs
:
Find p, replace s with 4
+ = 1
Multiply by 4p
4(3) + 3p = 4p
12 = 4p - 3p
p = 12 hrs
:
Find k, replace p with 12
+ = 1
multiply by 12k
12(4) + 4k = 12k
48 = 12k - 4k
k =
k = 6 hrs
:
Sumarize: k=6 hrs, p=12 hrs, s=4 hrs
:
Check solution in the 1st equation:
+ + =
+ + = 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
+ = 1
multiply by 12
2t + 3t = 12
5t = 12
t =
t = 2.4 hrs, K and S working together

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