$A$ bike covers a certain distance at a speed of $64 \, km/h$ in $8 \, hours$. If the bike were to cover the same distance in approximately $6 \, hours$,at what approximate speed should the bike travel? (in $km/h$)

$A$ and $B$ walk around a circular track. They start at $8\, a.m.$ from the same point in opposite directions. $A$ and $B$ walk at a speed of $2\, \text{rounds per hour}$ and $3\, \text{rounds per hour}$ respectively. How many times shall they cross each other before $9.30\, a.m.$?

$A$ man travels first $50 \, km$ at $25 \, kmph$, next $40 \, km$ at $20 \, kmph$, and then $90 \, km$ at $15 \, kmph$. His average speed for the whole journey (in $kmph$) is:

Two cars $P$ and $Q$ start at the same time from $A$ and $B$ which are $120 \, km$ apart. If the two cars travel in opposite directions,they meet after $1 \, hour$,and if they travel in the same direction (from $A$ towards $B$),then $P$ meets $Q$ after $6 \, hours$. What is the speed of car $P$ (in $km/hr$)?

$A$ thief is spotted by a policeman from a distance of $200 \text{ meters}$. When the policeman starts to chase the thief,the thief also starts running. Assuming the speed of the thief is $10 \text{ km/h}$ and that of the policeman is $12 \text{ km/h}$,how far will the thief have run before he is overtaken by the policeman? (in $\text{km}$)

$A$ train crosses a pole in $10 \, s$ and a platform,which is $40 \%$ longer than the length of the train,in $24 \, s$. If the length of the platform is $140 \, m$,what is the speed of the train in $m/s$?