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?
:
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
:
{{{12/t}}} + {{{12/((t+10))}}} = 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