College Algebra, Chapter 2, 2.5, Section 2.5, Problem 34

The power $P$(measured in horse power, $hp$) needed to propel a boat is directly proportional to the cube of the speed $s$. An $80-hp$ engine is needed to propel a certain boat at $10$ knots. Find the power needed to drive the boat at 15 knots.

$\begin{equation} \begin{aligned} P &= k s^3 && \text{model}\\ \\ 80 hp &= k \left( 10 \text{ knots}\right)^3 && \text{Substitute the given, solve for } k \\ \\ k &= \frac{80 hp}{\left( 10 \text{ knots}\right)^3} = \frac{80hp}{1000 \text{ knots}^3} = \frac{2}{25} \frac{hp}{\text{ knots}^3} \end{aligned} \end{equation}$

Then if $s = 15$ knots,

$\begin{equation} \begin{aligned} P &= k s^3 && \text{Model}\\ \\ P &= \frac{2}{25} \frac{hp}{ \text{knots}^3} \left( 15 \text{ knots}\right)^3 && \text{Solve for } P \text{, cancel out like terms}\\ \\ P &= 270 hp \end{aligned} \end{equation}$