SOLUTION: to do a work independently B requires six days more than what A requires. if they work together ,it will take two days less than what A alone takes.in how many days can B alone com

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Question 102576: to do a work independently B requires six days more than what A requires. if they work together ,it will take two days less than what A alone takes.in how many days can B alone complete the work?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation is:
(A's rate alone) + (B's rate alone) = (A & B rates working together)
or, in other words
(1 job / A's time) + (1 job / B's time) = 1 job / time working together
Let A = A's time to complete job alone
Let B = B's time to complete job alone
The problem says B = A + 6
and time working together = A - 2
1%2FA+%2B+1%2F%28A+%2B+6%29+=+1%2F%28A+-+2%29
multiply both sides by A%28A+%2B+6%29%28A+-+2%29
%28A+%2B+6%29%28A+-+2%29+%2B+A%28A+-+2%29+=+A%28A+%2B+6%29
A%5E2+%2B+6A+-2A+-+12+%2B+A%5E2+-+2A+=+A%5E2+%2B+6A
Subtract A%5E2+%2B+6A from both sides
A%5E2+-+4A+-+12+=+0
%28A+%2B+2%29%28A+-+6%29+=+0
A+=+-2 and A+=+6 are the solutions, but you can
discard the negative one
So, A gets the job done in 6 days working alone
B took six days more than A working alone
or, B takes 12 days working alone
To verify,
A = 6
B = 12
1%2FA+%2B+1%2F%28A+%2B+6%29+=+1%2F%28A+-+2%29
1%2F6+%2B+1%2F12+=+1%2F4 is this true?
2%2F12+%2B+1%2F12+=+3%2F12 yes, it's true