SOLUTION: A can finish a certain job in 10 days if B will help for 6 days. The same work can be done by B in 12 days if A helps for 6 days. If they work together, how long will it take for t

Question 971641: A can finish a certain job in 10 days if B will help for 6 days. The same work can be done by B in 12 days if A helps for 6 days. If they work together, how long will it take for them to do the job?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A can finish a certain job in 10 days if B will help for 6 days.
The same work can be done by B in 12 days if A helps for 6 days.

:
let a = time required by A working alone
let b = time required by B working alone
let the completed job = 1
:
Write an equation for each scenario scenario
+ = 1
+ = 1
Use elimination, multiply the 1st equation by 2, subtract the 2nd equation
+ = 2
+ = 1
------------------Subtraction eliminates b, find a
= 1
multiply by a
14 = a
A requires 14 hrs to do the job alone
:
Find b using + = 1; replace a with 14
+ = 1
multiply eq by 14b
10b + 14(6) = 14b
84 = 14b - 10b
84 = 4b
b = 84/4
b = 21 hrs for B to do the job alone
:
"If they work together, how long will it take for them to do the job?"
let t = time required when working together
+ = 1
multiply both sides by 42, cancel the denominators and you we have
3t + 2t = 42
5t = 42
t = 42/5
t = 8.4 hrs working together

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