How to solve this Quadratic Word problem? This is the word problem. 
If they work together, John and Vince can finish their project in Biology in two days. If they worked individually, it will take John three days longer than Vince to complete the task. How long will it take each to do the job alone?
Thanks in advance ;)
 A: Let $p$ be the total amount of hours necessary for the project. Let $j$ and $v$ be the amount of constant hours per day that John and Vince can contribute to the project respectively. Furthermore, we have also to assume, that both persons are additively productive, which might not be the case in the real world :).
Both sentences translate to the equations
\begin{align}
2(j+v)&=p\\
\frac{p}{v}-\frac{p}{j} &= 3
\end{align}
and we have to find $t_v = p/v$ and $t_j = p/j$ which is the amount of days john and vince need to complete the project individually (again under the assumption their productivity can be superpositioned). The equations for those variables now become
\begin{align}
2(\frac{1}{t_j}+\frac{1}{t_v})&=1\\
t_v-t_j &= 3
\end{align}
Multiply both equations and obtain
\begin{align}
&&(\frac{1}{t_j}+\frac{1}{t_v})(t_v-t_j) &=\frac{3}{2}\\
\Leftrightarrow&&(t^2_v-t^2_j) &=\frac{3}{2}t_vt_j\\
\end{align}
Plugging in $t_v = 3+t_j$ yields:
\begin{align}
((3+t_j)^2-t^2_j) &=\frac{3}{2}(3+t_j)t_j\\
\end{align}
Now you can further simplify it and solve the resulting quadratic equation for $t_v$ and yield $t_j$.
A: Vince needs $x$ days for the task, John $x+3$. This means that Vince completes ${1\over x}$ projects per day, and John ${1\over x+3}$. Together they complete ${1\over2}$ of a project per day, which leads to the equation
$${1\over x}+{1\over x+3}={1\over2}\ .$$
A: The project requires P units of work to complete. John works at a rate of J units of work per unit time. Vince works at a rate of V units of work per unit time. Then,
$P/(J+V)=2\text{ days}\Rightarrow\frac{1}{(P/J)^{-1}+(P/J)^{-1}}=2\text{ days},\text{and } P/J=P/V+3\text{ days}$
We now have two equations. We want to find $P/J$ and $P/V$ which are the times it would take each to do the job. We can recast it in terms of x and y if you wish, letting $x=P/J$ and $y=P/V$ we have
$1=(2\text{ days})(x^{-1}+y^{-1}),\text{ and } x=y+3\text{ days}$. Solve for x and y.
This gives y=P\V=3 days and x=P\J=6 days.
