Question 1197748
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When A,B and C work together, they can finish installing the garden in 3 days. 
The job could be completed of A worked 4 days alone and C worked 10 days alone 
or if B worked 5 days alone and C worked 3 days alone. 
How many days would it take each worker alone to complete the garden?
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<pre>
Let  "a"  be the A's rate of work, in job per day;

     "b"  be the B's rate of work, in job per day;

     "c"  be the C's rate of work, in job per day.


From the condition, we have this system of 3 equations in 3 unknowns

    a + b + c = {{{1/3}}},           (1)

    4a + 10c = 1,             (2)


    5b +  3c = 1.             (3)


To solve, express  a = {{{(1-10c)/4}}}  from (2), and express  b = {{{(1-3c)/5}}}  from (3).

Substitute these expressions into equation (1).  You will exclude "b" and "c" from (1)
and will get single equation for unknown "c"


    {{{(1-10c)/4}}} + {{{(1-3c)/5}}} + c = {{{1/3}}}.      (4)


Multiply both sides by 60


    15(1-10c) + 12*(1-3c) + 60c = 20

    15 - 150c + 12 - 36c + 60c = 20

    27 - 126c = 20

    27 - 20 = 126c

       7    = 126c

       c    = {{{7/126}}} = {{{1/18}}}.


It means that C will complete the job in 18 days working alone.


Now   a = {{{(1-10/18)/4}}} = {{{((8/18))/4}}} = {{{2/18}}} = {{{1/9}}};

      b = {{{(1-3/18)/5}}} = {{{((15/18))/5}}} = {{{3/18}}} = {{{1/6}}}.


<U>ANSWER</U>.  A can complete the job in 9 days working alone;

         B can complete the job in 6 days working alone;

         C can complete the job in 18 days working alone.
</pre>

Solved.