In rain man with the umbrella at an angle 45° to the vertical.

velocity of rain = v₁
velocity of man = v₂

⇒ Tanθ = v₂/v₁
⇒ Tan 45° = v₂/v₁
⇒ 1/√2 = v₂/v₁
⇒ v₁/v₂=√2/1
⇒ v₁: v₂=√2: 1