$A$ man takes $6\, h \, 15\, min$ in walking a distance and riding back to the starting place. He could walk both ways in $7\, h \, 45\, min$. The time taken by him to ride both ways is:

$A$ person sets out to cover a distance of $12 \, km$ in $45 \, minutes$. If he covers $\frac{3}{4}$ of the distance in $\frac{2}{3}$ of the time,what should be his speed to cover the remaining distance in the remaining time? (in $km/h$)

Walking $\frac{6}{7}$ of his usual speed, a man is $12 \, \text{minutes}$ late. The usual time taken by him to cover that distance is

Two men $A$ and $B$ walk from $P$ to $Q$ at a distance of $21 \text{ km}$ at speeds of $3 \text{ km/h}$ and $4 \text{ km/h}$ respectively. $B$ reaches $Q$ and returns immediately and meets $A$ at $R$. The distance from $P$ to $R$ is (in $\text{km}$):

Two trains start at the same time from Mumbai and Pune and proceed towards each other at the speeds of $60\, km/h$ and $40\, km/h$, respectively. When they meet, it is found that one train has travelled $20\, km$ more than the other. Find the distance between Mumbai and Pune (in $km$).

$A$ person travels from $P$ to $Q$ at a speed of $40 \, km/h$ and returns from $Q$ to $P$ by increasing his speed by $50\%$. What is his average speed for the entire journey? (in $km/h$)