Question 145847
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? 
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Let the completed job = 1
Let A = time required for A to complete it alone
Let B = time required for B to do it.
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Working together equation:
{{{6/A}}} + {{{6/B}}} = 1
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Each doing part of the job alone equation:
{{{3/A}}} + {{{10/B}}} = 1
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Use elimination here:
Multiply the above equation by 2 and subtract the 1st equation from it:
{{{6/A}}} + {{{20/B}}} = 2
{{{6/A}}} + {{{6/B}}} = 1
----------------------------subtracting eliminates A
0 + {{{14/B}}} = 1
B = 14 days working alone
:
Find A using the working together equation, substitute 14 for B
{{{6/A}}} + {{{6/14}}} = 1
Multiply equation by 14A to get rid of the denominators
6(14) + 6A = 14A
84 = 14A - 6A
A = {{{84/8}}}
A = 10.5 days working alone
:
:
Check solution using the 2nd equation (with a calc):
{{{3/10.5}}} + {{{10/14}}} = 1
.2857 + .7143 = 1