To a man walking at the rate of 3 km/hr the rain appears to fall vertically. When he increases the speed to 6 km/hr it appears to meet him at an angle of $45^{\circ}$ with vertical. Find the speed of rain.

Question

$$(a)\;3 km/hr\quad (b)\;\frac{3}{\sqrt 2} km/hr \quad (c)\;5km/hr \quad (d)\;3 \sqrt 2 km/hr$$