Chapter 9, Problem 25RP

To determine

Tofind: For a boy whetheris it easy to swim directly across the lake and then walk to the golden arches or to swim directly to the golden arches. .

Answer to Problem 25RP

It is easy to swim across and then walk for a boy.

Explanation of Solution

Given information:

A boy standing on the shore of a lake 1 miles wide wants to reach the golden arches which is 3 miles down the shore on the opposite side of the lake.

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

To swim directly:

  $\begin{array}{l}{\left(x\right)}^2={\left(1\right)}^2+{\left(3\right)}^2\\ {\left(x\right)}^2=1+9\\ x=\sqrt{10}\end{array}$

  $\sqrt{10}$ miles at 2mph would be $\frac{\sqrt{10}}{2}$ or approximately $1\frac{1}{2}$ hours.

To swim across and walk:

one mile swimming at $2mph=\frac{1}{2}hour.$

Three miles walking at $4mph=\frac{3}{4}hour.$

Total time = $\frac{1}{2}+\frac{3}{4}=1\frac{1}{4}hours.$

To swim directly it takes $1\frac{1}{2}$ hours.

To swim across and walk it takes $1\frac{1}{4}hours$ .

It is easy to swim across and then walk for a boy.