Two cars $A$ and $B$ travel from one city to another,at speeds of $72\, km/hr$ and $90\, km/hr$ respectively. If car $B$ takes $1\, hour$ less than car $A$ for the journey,what is the distance (in $km$) between the two cities?

$A$ train of $320 \, m$ crosses a platform in $24 \, s$ at a speed of $120 \, km/h$. $A$ man crosses the same platform in $4 \, min$. What is the speed of the man in $m/s$?

The speeds of $A$ and $B$ are in the ratio of $3: 4$. $A$ takes $20 \, min$ more than $B$ to reach a destination. Find the time in which $A$ reaches the destination.

Two trains are moving in the same direction at $50 \, km/h$ and $30 \, km/h$. The faster train crosses a man in the slower train in $18 \, seconds$. Find the length of the faster train (in $m$).

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 $a.m.$)

The speed of a train going from Nagpur to Allahabad is $100 \text{ km/h}$,while its speed is $150 \text{ km/h}$ when coming back from Allahabad to Nagpur. What is the average speed during the whole journey in $\text{km/h}$?