<PRE><B>Question 579436</B>
A takes 10 days less than the time B to complete a work.
 If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
:
Let b = time for B to complete the work
then
(b-10) = time for A to do it
:
Let the completed job = 1
:
A typical shared work equation
:
{{{12/b}}} + {{{12/((b-10))}}} = 1
Multiply by b(b-10)
b(b-10)*{{{12/b}}} + b(b-10)*{{{12/((b-10))}}} = b(b-10)
Cancel the denominators
12(b-10) + 12b = b^2 - 10b
:
12b - 120 + 12b = b^2 - 10b
Combine like terms on the right
0 = b^2 -10b - 24b + 120 
b^2 - 34b + 120 = 0
this will factor to
(b-30)(b-4) = 0
Two solutions
b = 4
and
b = 30 days, this is the only reasonable answer
;
:
See if checks out
12/30 + 12/20 -
.4 + .6 = 1, confirms our solution of b = 30 days</PRE>