College Algebra, Chapter 1, 1.3, Section 1.3, Problem 104

Jan, Krix and Aja deliver advertising flyers in a small town. If each person works alone, it takes Jan $4h$ to deliver all the flyers, and it takes Aja in longer than it take Krix. Working together, they can deliver all the flyers in $40\%$ of the time it takes Krix working alone. How long does it take Krix to deliver all the flyers alone?

If we let $x$ be the time it takes Krix to work alone, then $x + 1$ will be the time it takes Aja to do the same work. So, the total work will be..


$
\begin{equation}
\begin{aligned}

\frac{1}{4} + \frac{1}{x} + \frac{1}{x + 1} =& \frac{1}{0.40x}
&& \text{Model}
\\
\\
\frac{x(x + 1) + 4(x + 1) + 4x}{4x (x + 1)} =& \frac{1}{0.40x}
&& \text{Get the LCD}
\\
\\
\frac{x^2 + x + 4x + 4 + 4x}{4x (x + 1)} =& \frac{1}{0.40x}
&& \text{Apply Distributive Property}
\\
\\
\frac{x^2 + 9x + 4}{4x (x + 1)} =& \frac{1}{0.40 x}
&& \text{Simplify the numerator}
\\
\\
0.40(x^2 + 9x + 4) =& 4(x + 1)
&& \text{Apply cross multiplication and cancel out $x$ in the denominator}
\\
\\
0.40x^2 + 3.6x + 1.6 =& 4x + 4
&& \text{Simplify}
\\
\\
0.40x^2 - 0.40x - 2.40 =& 0
&& \text{Combine like terms}
\\
\\
x^2 - x - 6 =& 0
&& \text{Divide with both sides by } 0.40
\\
\\
(x - 3)(x + 2) =& 0
&& \text{Factor out}
\\
\\
x - 3 =& 0 \text{ and } x + 2 = 0
&& \text{ZPP}
\\
\\
x =& 3 \text{ and } x = -2
&& \text{Solve for } x
\\
\\
x =& 3 hrs
&& \text{Choose } x > 0

\end{aligned}
\end{equation}
$


Thus, it takes 3 hours for Krix to do the work alone.