Chapter 6.4, Problem 5CYU

To determine

To determine the speed of kayak in still water

Answer to Problem 5CYU

The speed of kayak in still water is 6 miles per hour.

Explanation of Solution

Given:

A kayak moves 16 miles downstream in 2 hours and moves 16 miles upstream in 4 hours.

Formula used:

  $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Calculation:

Let,

The speed of kayak in still water be x miles per hour

The speed of stream of water is y miles per hour.

Hence,

The speed of kayak upstream will be $\left(x-y\right)$ miles per hour

The speed of kayak downstream will be $\left(x+y\right)$ miles per hour

A kayak moves 16 miles downstream in 2 hours, which means,

  $\begin{array}{l}x+y=\frac{16}{2}\\ \Rightarrow x+y=8\end{array}$

And, a kayak moves16 miles upstream in 4 hours, which means,

  $\begin{array}{l}x-y=\frac{16}{4}\\ \Rightarrow x-y=4\end{array}$

Let the equation,

  $x+y=\mathrm{8.......}(i)$

  $x-y=\mathrm{4......}(ii)$

Now, add equation ( i ) and equation ( ii ),

  $\begin{array}{l}\Rightarrow (x+y)+(x-y)=8+4\\ \Rightarrow 2x=12\\ \Rightarrow x=\frac{12}{2}\\ \Rightarrow x=6\end{array}$

Conclusion:

Therefore, the speed of kayak in still water is 5 miles per hour.