Question

Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was \[15\sqrt{2}\]

 km. Find their speed per hour.

 

Answer 1

It is given that, Pranali and Prasad have same speed.
Thus, they cover same distance in 2 hours.
i.e. OA = OB

Let the speed be x km per hour.

According to Pythagoras theorem,
In ∆AOB

\[{AB}^2 = {AO}^2 + {OB}^2 \]
\[ \Rightarrow \left( 15\sqrt{2} \right)^2 = {AO}^2 + {OA}^2 \]
\[ \Rightarrow 450 = 2 {AO}^2 \]
\[ \Rightarrow {AO}^2 = \frac{450}{2}\]
\[ \Rightarrow {AO}^2 = 225\]
\[ \Rightarrow AO = 15 km\]
\[ \Rightarrow BO = 15 km\]

\[\text{Speed} = \frac{Distance}{Time}\]
\[ = \frac{15}{2}\]
\[ = 7 . 5 \text{km per hour}\]