Answer
7.2 hours for small pipe, 5.2 hours for large pipe
Work Step by Step
large pipe: 2 hours less than the small pipe (x-2)
small pipe: x hours
together: 3 hours
$1/(x-2) + 1/x = 1/3$
$1*(x-2)*x*3/(x-2) + 1*(x-2)*x*3/x = 1*(x-2)*x*3/3$
$3x +3(x-2) = x(x-2)$
$3x+3x-6=x^2-2x$
$6x-6=x^2-2x$
$8x-6=x^2$
$x^2-8x+6=0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-(-8)±\sqrt {(-8)^2-4*1*6})/2*1$
$x=(8±\sqrt {64-24})/2$
$x=(8±\sqrt {40})/2$
$x=(8±6.32)/2$
$x=(8±6.32)/2$
$x=(8+6.32)/2$
$x=14.32/2$
$x=7.16$
$x=(8±6.32)/2$
$x=(8-6.32)/2$
$x=1.68/2$
$x=.84$ (this is less than two hours, so this answer is not valid)
$7.16-2$
$5.16$
