SOLUTION: 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

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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      Log On


   

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 workA 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
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Ft + 4%2F%28%28t-6%29%29 = 1
multiply by t(t-6)
t(t-6)*4%2Ft + t(t-6)*4%2F%28%28t-6%29%29 = 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%2F12 + 4%2F%28%2812-6%29%29 =
1%2F3 + 2%2F3 = 1