Chapter 9, Problem 23RP

To determine

Tocalculate:The distance between two boats at noon.

Answer to Problem 23RP

The distance between two boats at noon is 75 km.

Explanation of Solution

Given information:

Two boats leave the harbor at 9.00 A.M. Boat A sails north at 20 km/hr.Boat B sails west at 15 km/hr.

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,

  $a^2+b^2\text{= }{c}^2$

Calculation:

  

The boats A and B cover the distance at ratio of $\frac{4}{3}.$ So Boat A traveled 60 km, Boat B traveled 45 km.

Boats travel for 3 hours(9.00 A.M to 12.00 A.M).Noon begins from 12.00 P.M.

  $\begin{array}{l} 60=\left(20\right)\left(3\right),\\ 45=\left(15\right)\left(3\right)\end{array}$

The distance between the boats is the hypotenuse of a right triangle AHB .

In right angle $\Delta AHB$ ,we get

  $\begin{array}{l}{\left(AB\right)}^2={\left(AH\right)}^2+{\left(HB\right)}^2\\ {\left(AB\right)}^2={60}^2+{45}^2\\ AB=\sqrt{3600+2025}\\ AB=\sqrt{5625}\\ AB=75\end{array}$

The distance between two boats at noon is 75 km