$A$ boat running downstream covers a distance of $16 \, km$ in $2 \, hours$, while for covering the same distance upstream, it takes $4 \, hours$. What is the speed of the boat in still water?

$A$ boat is moving with a velocity of $3\hat i + 4\hat j$ in a river,and the water is moving with a velocity of $-3\hat i - 4\hat j$ with respect to the ground. The relative velocity of the boat with respect to the water is:

$A$ bus appears to go with a speed of $25 \, km/hr$ to a car driver,driving at the rate of $7 \, km/hr$ northwards. If the bus actually travels in the east direction,its speed is ......... $km/h$.

On a long horizontally moving belt,a child runs to and fro with a speed $9 \; km \; h^{-1}$ (with respect to the belt) between his father and mother located $50 \; m$ apart on the moving belt. The belt moves with a speed of $4 \; km \; h^{-1}$. For an observer on a stationary platform outside,what is the:
$(a)$ speed of the child running in the direction of motion of the belt?
$(b)$ speed of the child running opposite to the direction of motion of the belt?
$(c)$ time taken by the child in $(a)$ and $(b)$?
Which of the answers alter if motion is viewed by one of the parents?

$A$ river of width $200 \ m$ is flowing from west to east with a speed of $18 \ km/h$. $A$ boat,moving with a speed of $36 \ km/h$ in still water,is made to travel one round trip (bank to bank of the river). The minimum time taken by the boat for this journey and the displacement along the river bank are . . . . . . and . . . . . . respectively.

Two trains,each of length $100 \, m$,are moving parallel towards each other at speeds of $72 \, km/h$ and $36 \, km/h$ respectively. In how much time will they cross each other (in $, s$)?