$A$ man goes from a place $A$ to $B$ at a speed of $12 \, km/hr$ and returns from $B$ to $A$ at a speed of $18 \, km/hr$. The average speed for the whole journey is (in $km/hr$):

Rajesh covers a certain distance by bus at $16 \text{ km/h}$ and returns to the starting point on a cycle at $9 \text{ km/h}$. His average speed for the whole journey is (in $\text{km/h}$):

$A$ man with $\frac{3}{5}$ of his usual speed reaches the destination $2 \frac{1}{2}$ hours late. Find his usual time to reach the destination? (in $hours$)

$A$ and $B$ are two towns. $A$ car goes from $A$ to $B$ at a speed of $64 \, km/h$ and returns to $A$ at a slower speed. If its average speed for the whole journey is $56 \, km/h$,find its return speed (in $km/h$).

What is the length of the bridge (in $m$) that a man riding at $15 \, km/h$ can cross in $5 \, minutes$?

$A$ thief is stopped by a policeman from a distance of $150\, m$. When the policeman starts the chase,the thief also starts running. Assuming the speed of the thief as $7\, km/h$ and that of the policeman as $9\, km/h$,how far would the thief have run before he is overtaken by the policeman? (in $m$)