Chapter 6.4, Problem 3GP

To determine

To determine the speed of boat in still water

Answer to Problem 3GP

The speed of boat in still water is 3.33 miles per hour.

Explanation of Solution

Given:

A canoeist moves 4 miles downstream in 1 hour and moves 4 miles upstream in 1.5 hour.

Formula used:

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

Calculation:

Let,

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

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

Hence,

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

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

A canoeist moves 4miles downstream in 1 hour, which means,

$\begin{array}{l}x+y=\frac{4}{1}\\ \Rightarrow x+y=4\end{array}$

And, q canoeist moves 4 miles upstream in 1.5 hour, which means,

$\begin{array}{l}x-y=\frac{4}{1.5}\\ \Rightarrow x-y=2.67\end{array}$

Let the equation,

$x+y=\mathrm{4.......}(i)$

$x-y=\mathrm{2.67......}(ii)$

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

$\begin{array}{l}\Rightarrow (x+y)+(x-y)=4+2.67\\ \Rightarrow 2x=6.67\\ \Rightarrow x=\frac{6.67}{2}\\ \Rightarrow x=3.33\end{array}$

Conclusion:

Therefore, the speed of boat in still water is 3.33 miles per hour.