SOLUTION: Brain and David can finish the job in 12 days if they work together. If only one of them works on a job, David will take 10 days longer than Brain. How many days does David need to

Question 540710: Brain and David can finish the job in 12 days if they work together. If only one of them works on a job, David will take 10 days longer than Brain. How many days does David need to finish the job alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Brain and David can finish the job in 12 days if they work together.
If only one of them works on a job, David will take 10 days longer than Brain.
How many days does David need to finish the job alone?
:
Let t = time required by Brian working alone
then
(t+10) = time required by David
:
Let the completed job = 1
:
Each will do a fraction of the job, the two fractions add up to 1
:
+ = 1
multiply by t(t+10), results:
12(t+10) + 12t = t(t+10)
12t + 120 + 12t = t^2 + 10t
24t + 120 = t^2 + 10t
0 = t^2 + 10t - 24t - 120
A quadratic equation
t^2 - 14t - 120 = 0
(t-20)(t+6) = 0
the positive solution
t = 20 days for Brian to do the job
I'll let you figure out how many days that David will required

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