$A$ man goes $10\,km$ downstream in $2\,hrs$ and $30\,km$ upstream in $10\,hrs$. How much time will he take to swim $40\,km$ in still water?

Rain is falling vertically with a speed of $30 \,m/s$. A man rides a bicycle with a speed of $10 \,m/s$ from East to West direction. At what angle with the vertical does he see the rain falling?

In a harbour,wind is blowing at the speed of $72 \; km/h$ and the flag on the mast of a boat anchored in the harbour flutters along the $N-E$ direction. If the boat starts moving at a speed of $51 \; km/h$ to the north,what is the direction of the flag on the mast of the boat?

On a two-lane road,car $A$ is travelling with a speed of $36 \; km/h$. Two cars $B$ and $C$ approach car $A$ in opposite directions with a speed of $54 \; km/h$ each. At a certain instant,when the distance $AB = AC = 1 \; km$,car $B$ decides to overtake car $A$ before car $C$ does. What minimum acceleration (in $m/s^2$) of car $B$ is required to avoid an accident?

It takes $1$ minute for a passenger standing on an escalator to reach the top. If the escalator does not move,it takes him $3$ minutes to walk up. How many seconds will it take for the passenger to arrive at the top if he walks up the moving escalator?

Two towns $A$ and $B$ are connected by a regular bus service with a bus leaving in either direction every $T$ minutes. $A$ man cycling with a speed of $20 \; km/h$ in the direction $A$ to $B$ notices that a bus goes past him every $18 \; min$ in the direction of his motion,and every $6 \; min$ in the opposite direction. What is the period $T$ (in $min$) of the bus service and with what speed (assumed constant) do the buses ply on the road?