SOLUTION: Hi, I am having difficulty putting this problem into an equation even though I know the answer. Workman A and B complete a certain job if they work together for 6 days or if A alo

Question 145847: Hi, I am having difficulty putting this problem into an equation even though I know the answer.
Workman A and B complete a certain job if they work together for 6 days or if A alone works for 3 days and B alone works for 10 days. How long does it take each man to complete the job alone?
The answer is A - 10 1/2 days and B - 14 days
Thank you for your help.
Found 2 solutions by ankor@dixie-net.com, scott8148:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Workman A and B complete a certain job if they work together for 6 days or if A alone works for 3 days and B alone works for 10 days. How long does it take each man to complete the job alone?
:
Let the completed job = 1
Let A = time required for A to complete it alone
Let B = time required for B to do it.
:
Working together equation:
+ = 1
:
Each doing part of the job alone equation:
+ = 1
:
Use elimination here:
Multiply the above equation by 2 and subtract the 1st equation from it:
+ = 2
+ = 1
----------------------------subtracting eliminates A
0 + = 1
B = 14 days working alone
:
Find A using the working together equation, substitute 14 for B
+ = 1
Multiply equation by 14A to get rid of the denominators
6(14) + 6A = 14A
84 = 14A - 6A
A =
A = 10.5 days working alone
:
:
Check solution using the 2nd equation (with a calc):
+ = 1
.2857 + .7143 = 1

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let x="A time alone" and y="B time alone"

"Workman A and B complete a certain job if they work together for 6 days"
__ 6/x+6/y=1

"A alone works for 3 days and B alone works for 10 days" __ 3/x+10/y=1
__ multiplying by 2 __ 6/x+20/y=2

subtracting equations __ 6/x+20/y-(6/x+6/y)=2-1 __ 14/y=1 __ 14=y

substituting __ 6/x+6/14=1 __ subtracting 6/14 __ 6/x=8/14 __ multiplying by 14x __ 84=8x
__ dividing by 8 __ 10.5=x
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