## 2442.52 – Daniel Boone on Plum Creek

Daniel Boone can paddle his canoe at 15 mph in still water. However, he is paddling on Plum Creek, which, after a heavy rain, rages along at 5 mph. He paddles downriver for a while, then turns around and (with difficulty) paddles back upstream to his starting point. What is his average speed for the entire trip?

## Solution

We make our trusty table (see the figure below). Note that Daniel's rates are 15 + 5 and 15 - 5.

Now we solve for $r$:

$\begin{aligned}
r &=& \frac{2d}{\frac{d}{20} + \frac{d}{10}} \\
&=& \frac{2d}{\frac{3d}{20}} = 2d \cdot \frac{20}{3d} \\
&=& \frac{40}{3} = 13 \frac{1}{3} \text{ mph}.
\end{aligned}$

The answer is $13.33\ldots$ mi/hr—not the 15 miles per hour we might expect.