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
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-> 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
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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
