Answer
$t=5.2$ hours
Work Step by Step
The formula for working with a friend in $y$ hours is given as a function of the $t$ hours it takes you to finish working alone.
$\frac{1}{t}+\frac{1}{t+2}=\frac{1}{y}$
Given $y=3$, to find $t$.
$\frac{1}{t}+\frac{1}{t+2}=\frac{1}{3}$
$\frac{t+2+t}{t^2+2t}=\frac{1}{3}$
$6t+6=t^2+2t$
$t^2-4t-6=0$
Solving the equation using quadratic formula for the quadratic equation...
$t=\frac{4\pm \sqrt {(-4)^2+4(1)(6)}}{2}=2\pm\sqrt {10}$,
thus, $t=5.2$ hours
