Question 1013984
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A takes 10 more days to do a job than B. They both do a job in 12 days. 
In how many days B will take to complete the work if he works alone??
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<pre>
Let a = # of days for A to do the job working alone, and
Let b = # of days for B to do the job working alone.

According to the condition, you have this system of two equations in two unknowns a and b:

a = b + 10,                 (1)

{{{12}}}.{{{(1/a + 1/b)}}} = 1.           (2)

From (1), substitute a = b + 10 into (2). You will get

{{{12}}}.{{{(1/(b+10) + 1/b)}}} = {{{1}}}.    (3)

In (3), multiply both sides by b*(b+10) to get off the denominators. You will get

12*b + 12*(b+10) = b*(b+10),   or

24b + 120 = {{{b^2 + 10b}}},    or

{{{b^2 + 10b - 24b - 120}}} = {{{0}}},   or

{{{b^2 - 14b - 120}}} = {{{0}}}.

Factor left side:

(b-20)*(b+6) = 0.

The roots are b = 20 and b = -6.

Only positive b = 20 fits the condition.

Then a = b + 10 = 30.

<U>Answer</U>. It will take 20 days for B to complete the job working alone.
</pre>

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