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?

$A$ man standing on a road has to hold his umbrella at $30^{\circ}$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \,km/h$. He finds that raindrops are hitting his head vertically. The actual speed of raindrops is:

$A$ swimmer swims in still water at a speed of $5 \text{ km/hr}$. He enters a $200 \text{ m}$ wide river,having a river flow speed of $4 \text{ km/hr}$,at point $A$ and proceeds to swim at an angle of $127^{\circ}$ $(\sin 37^{\circ} = 0.6)$ with the river flow direction. Another point $B$ is located directly across $A$ on the other side. The swimmer lands on the other bank at a point $C$,from which he walks the distance $CB$ with a speed of $3 \text{ km/hr}$. The total time in which he reaches from $A$ to $B$ is .......... $\text{minutes}$.

Two cars $A$ and $B$ are moving with the same speed of $45\,km/h$ along the same direction. If a third car $C$ coming from the opposite direction with a speed of $36\,km/h$ meets the two cars in an interval of $5\,min$,the distance of separation between the two cars $A$ and $B$ should be.......$km$.

Consider two observers observing a single moving object,and one observer observing two moving objects. Explain the concept of relative velocity in these scenarios.

Two parallel rail tracks run north-south. Train $A$ moves north with a speed of $54 \; km \; h^{-1},$ and train $B$ moves south with a speed of $90 \; km \; h^{-1}.$ What is the velocity of $B$ with respect to $A$?