SOLUTION: 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.

Question 579436: 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.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
:
+ = 1
Multiply by b(b-10)
b(b-10)* + b(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
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