SOLUTION: A takes 6 days less than the time taken by B to finish the piece of work.if A and B together can finish it in 4 days.then find the time taken by B to finish the work by himself?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A takes 6 days less than the time taken by B to finish the piece of work.if A and B together can finish it in 4 days.then find the time taken by B to finish the work by himself?      Log On


   

Question 800948: A takes 6 days less than the time taken by B to finish the piece of work.if A and B together can finish it in 4 days.then find the time taken by B to finish the work by himself?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform rates, task-completion problem!

The 1 job being done is, "finish a piece of work". The unit for rate iis jobs per day.

Agent B does the job in some unknown amount of time, call it d.
The rate for agent B is 1%2Fd Jobs per Day.
Agent A is faster. Agent A works at the rate of 1%2F%28d-6%29 jobs per day. Notice, "6 hours less than... B".

The rate for A and B working at the same time is 1%2F4 jobs per day. This is given.

Enough is known to determine "d" for the amount of time that agent B needs to do one job if alone. Their combined rate working together is simply additive.
highlight%28%281%2Fd%29%2B1%2F%28d-6%29=1%2F4%29
L.C.D. is like, 4d%28d-6%29.
4%28d-6%29%2B4d=d%28d-6%29
4d-24%2B4d=d%5E2-6d
d%5E2-6d=4d-24%2B4d
d%5E2-14d%2B24=0
General solution to a quadratic formula:
d=%2814%2Bsqrt%2814%5E2-4%2A24%29%29%2F2
d=%2814%2Bsqrt%2810%29%29%2F2
d=24%2F2
highlight%28d=12%29
.
..... You do the rest.