$A$ is faster than $B$. $A$ and $B$ each walk $24 \, km$. The sum of their speeds is $7 \, km/hr$ and the sum of the times taken by them is $14 \, hours$. Then $A$'s speed is equal to (in $km/hr$):

$A$ man travelled from the village to the post office at the rate of $25 \, km/hr$ and walked back at the rate of $4 \, km/hr$. If the whole journey took $5 \, hours \, 48 \, minutes$,find the distance of the post office from the village (in $km$).

In covering a certain distance,the speeds of $A$ and $B$ are in the ratio of $3:4$. $A$ takes $30 \text{ minutes}$ more than $B$ to reach the destination. The time taken by $A$ to reach the destination is (in $\text{hours}$):

$A$ bus started its journey from Bettiah and reached Motihari in $44 \, \text{min}$ with an average speed of $50 \, \text{km/h}$. If the average speed of the bus is increased by $5 \, \text{km/h}$, how much time will it take to cover the same distance? (in $\text{min}$)

It takes $8 \, \text{hours}$ for a $600 \, \text{km}$ journey if $120 \, \text{km}$ is covered by train and the rest by car. It takes $20 \, \text{minutes}$ more if $200 \, \text{km}$ is covered by train and the rest by car. The ratio of the speed of the train to that of the car is:

$A$ 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 $km/h$).