Question 102576
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/A + 1/(A + 6) = 1/(A - 2)}}}
multiply both sides by {{{A(A + 6)(A - 2)}}}
{{{(A + 6)(A - 2) + A(A - 2) = A(A + 6)}}}
{{{A^2 + 6A -2A - 12 + A^2 - 2A = A^2 + 6A}}}
Subtract {{{A^2 + 6A}}} from both sides
{{{A^2 - 4A - 12 = 0}}}
{{{(A + 2)(A - 6) = 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/A + 1/(A + 6) = 1/(A - 2)}}}
{{{1/6 + 1/12 = 1/4}}} is this true?
{{{2/12 + 1/12 = 3/12}}} yes, it's true