Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 52

A cyclist traveling at a constant speed completes $\displaystyle \frac{3}{5}$ of a trip in $\displaystyle 1 \frac{1}{2} h$. In how many additional hours will the cyclist complete the entire trip?

Recall that the formula that relates velocity $(v)$, distance $(d)$ and time $(t)$ is represented by

$\displaystyle v = \frac{d}{t}$

Then, if we let $d_1$ be the distance of the entire trip, we have


$
\begin{equation}
\begin{aligned}

v =& \frac{\displaystyle \frac{3}{5} d_1}{\displaystyle 1 \frac{1}{2}}
\\
\\
v =& \frac{\displaystyle \frac{3}{5} d_1}{\displaystyle \frac{3}{2}}
\\
\\
v =& \left( \frac{\cancel{3}}{5} d_1 \right) \left( \frac{2}{\cancel{3}} \right)
\\
\\
v =& \frac{2}{5} d_1

\end{aligned}
\end{equation}
$


And since the cyclist is traveling at a constant speed, we get


$
\begin{equation}
\begin{aligned}

v =& v
\\
\\
\frac{2}{5} d_1 =& \frac{d_1}{t}
\\
\\
\frac{2}{5} =& \frac{1}{t}
\\
\\
t =& \frac{5}{2} \text{ hours}

\end{aligned}
\end{equation}
$


In other words, in order for the cyclist to complete the trip, the additional hours must be spend is $\displaystyle \frac{5}{2} - 1 \frac{1}{2} = \frac{5}{2} - \frac{3}{2} = \frac{2}{2} = 1 $ hour.

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