Question 567310
A can finish the work in 6 days less than the time taken by B to finish the work.
If both of them together can finish it in 4 days, then find the time taken by B alone to finish the work. 
:
Let t = time required by B to do the work
then
(t-6) = time required by A to do it
:
Let the completed job = 1
:
A shared work equation
:
{{{4/t}}} + {{{4/((t-6))}}} = 1
multiply by t(t-6)
t(t-6)*{{{4/t}}} + t(t-6)*{{{4/((t-6))}}} = t(t-6)
cancel the denominators, resulting in
4t + 4(t-6) = t^2 - 6t
4t + 4t - 24 = t^2 - 6t
combine like terms on the right to form a quadratic equation
0 = t^2 - 6t - 8t + 24 
t^2 - 14t + 24 = 0
Factors to
(t-12)(t-2) = 0
Two solutions, but only one will make sense
t = 12 hrs for B to do the job alone. 
:
:
Check this
{{{4/12}}} + {{{4/((12-6))}}} = 
{{{1/3}}} + {{{2/3}}} = 1