document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #74587 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The equation is:
\n" ); document.write( "(A's rate alone) + (B's rate alone) = (A & B rates working together)
\n" ); document.write( "or, in other words
\n" ); document.write( "(1 job / A's time) + (1 job / B's time) = 1 job / time working together
\n" ); document.write( "Let A = A's time to complete job alone
\n" ); document.write( "Let B = B's time to complete job alone
\n" ); document.write( "The problem says B = A + 6
\n" ); document.write( "and time working together = A - 2
\n" ); document.write( " $\"1%2FA+%2B+1%2F%28A+%2B+6%29+=+1%2F%28A+-+2%29\"$
\n" ); document.write( "multiply both sides by $\"A%28A+%2B+6%29%28A+-+2%29\"$
\n" ); document.write( " $\"%28A+%2B+6%29%28A+-+2%29+%2B+A%28A+-+2%29+=+A%28A+%2B+6%29\"$
\n" ); document.write( " $\"A%5E2+%2B+6A+-2A+-+12+%2B+A%5E2+-+2A+=+A%5E2+%2B+6A\"$
\n" ); document.write( "Subtract $\"A%5E2+%2B+6A\"$ from both sides
\n" ); document.write( " $\"A%5E2+-+4A+-+12+=+0\"$
\n" ); document.write( " $\"%28A+%2B+2%29%28A+-+6%29+=+0\"$
\n" ); document.write( " $\"A+=+-2\"$ and $\"A+=+6\"$ are the solutions, but you can
\n" ); document.write( "discard the negative one
\n" ); document.write( "So, A gets the job done in 6 days working alone
\n" ); document.write( "B took six days more than A working alone
\n" ); document.write( "or, B takes 12 days working alone
\n" ); document.write( "To verify,
\n" ); document.write( "A = 6
\n" ); document.write( "B = 12
\n" ); document.write( " $\"1%2FA+%2B+1%2F%28A+%2B+6%29+=+1%2F%28A+-+2%29\"$
\n" ); document.write( " $\"1%2F6+%2B+1%2F12+=+1%2F4\"$ is this true?
\n" ); document.write( " $\"2%2F12+%2B+1%2F12+=+3%2F12\"$ yes, it's true \n" ); document.write( "

\n" );