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?

$A$ car covers $\frac{1}{5}$ of the distance from $A$ to $B$ at the speed of $8 \, km/h$,$\frac{1}{10}$ of the distance at $25 \, km/h$,and the remaining at the speed of $20 \, km/h$. Find the average speed of the whole journey in $km/h$. (in $.625$)

If a boy travels from his house to school at the rate of $4 \, km/h$,he reaches the school $10 \, minutes$ earlier than the scheduled time. However,if he walks at the rate of $3 \, km/h$,he reaches $10 \, minutes$ late. Find the distance of the school from his house (in $km$).

$A$ train can travel $50\%$ faster than a car. Both start from point $A$ at the same time and reach point $B$,$75\, km$ away from $A$,at the same time. On the way,however,the train lost about $12.5\, \text{minutes}$ while stopping at the stations. The speed of the car is (in $km/hr$):

If a man walks at the rate of $5\, km/h$,he misses a train by $7\, minutes$. However,if he walks at the rate of $6\, km/h$,he reaches the station $5\, minutes$ before the arrival of the train. The distance covered by him to reach the station is (in $km$)

Two guns were fired from the same place at an interval of $13 \text{ minutes}$,but a person in a train approaching the place hears the second shot $12 \text{ minutes } 30 \text{ seconds}$ after the first. Find the speed of the train,assuming that sound travels at $330 \text{ m/s}$ (in $\text{km/hr}$).