How many seconds will a $500 \, m$ long train take to cross a man walking with a speed of $3 \, km/h$ in the direction of the moving train, if the speed of the train is $63 \, km/h$?

The distance between two cities $A$ and $B$ is $330\, km$. $A$ train starts from $A$ at $8\, a.m.$ and travels towards $B$ at $60\, km/hr$. Another train starts from $B$ at $9\, a.m.$ and travels towards $A$ at $75\, km/hr$. At what time do they meet? (in $a.m.$)

Two places $P$ and $Q$ are $162 \, km$ apart. $A$ train leaves $P$ for $Q$ and simultaneously another train leaves $Q$ for $P$. They meet at the end of $6 \, hours$. If the former train travels $8 \, km/h$ faster than the other,then the speed of the train from $Q$ is (in $km/h$):

Two trains are running in opposite directions with the same speed. If the length of each train is $135 \, m$ and they cross each other in $18 \, s$,the speed of each train is (in $km/h$):

$A$ man covers a certain distance between his house and office on a scooter. With an average speed of $30 \, km/hr$,he is late by $10 \, min$. However,with a speed of $40 \, km/hr$,he reaches his office $5 \, min$ earlier. Find the distance between his house and office in $km$.

An aeroplane covers a certain distance at a speed of $240 \text{ km/h}$ in $5 \text{ hours}$. To cover the same distance in $1 \frac{2}{3} \text{ hours}$,it must travel at a speed of (in $\text{km/h}$):