#### 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.

#### Solution

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

\[{AB}^2 = {AO}^2 + {OB}^2 \]

\[ \Rightarrow \left( 15\sqrt{2} \right)^2 = {AO}^2 + {OA}^2 \]

\[ \Rightarrow 450 = 2 {AO}^2 \]

\[ \Rightarrow {AO}^2 = \frac{450}{2}\]

\[ \Rightarrow {AO}^2 = 225\]

\[ \Rightarrow AO = 15 km\]

\[ \Rightarrow BO = 15 km\]

\[\text{Speed} = \frac{Distance}{Time}\]

\[ = \frac{15}{2}\]

\[ = 7 . 5 \text{km per hour}\]

Is there an error in this question or solution?

Solution 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 √ 2 Km. Find Their Speed per Hour. Concept: Pythagoras Theorem.