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

$$\begin{gathered} {\mathrm{AB}}^2={\mathrm{AO}}^2+{\mathrm{OB}}^2 \\ \Rightarrow {\left(15\sqrt{2}\right)}^2={\mathrm{AO}}^2+{\mathrm{OA}}^2 \\ \Rightarrow 450=2{\mathrm{AO}}^2 \\ \Rightarrow {\mathrm{AO}}^2=\frac{450}{2} \\ \Rightarrow {\mathrm{AO}}^2=225 \\ \Rightarrow \mathrm{AO}=15\mathrm{km} \\ \Rightarrow \mathrm{BO}=15\mathrm{km} \end{gathered}$$

$$\begin{gathered} \mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}} \\ =\frac{15}{2} \\ =7.5\mathrm{km}\mathrm{per}\mathrm{hour} \end{gathered}$$

Hence, their speed is 7.5 km per hour.