$A$ train covers a distance in $50 \text{ minutes}$ if it runs at a speed of $48 \text{ km/h}$. The speed at which the train must run to reduce the time of journey to $40 \text{ minutes}$ will be (in $\text{km/h}$):

Mohan walks from Tilak Nagar to Moti Nagar and back in a certain time at the rate of $3 \frac{1}{2} \, km/h$. But,if he had walked from Tilak Nagar to Moti Nagar at the rate of $3 \, km/h$ and back from Moti Nagar to Tilak Nagar at the rate of $4 \, km/h$,he would have taken $10 \, minutes$ longer. The distance between Tilak Nagar and Moti Nagar is (in $km$)

In a flight of $600 \, km$,an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by $200 \, km/hr$ and the time of flight increased by $30 \, minutes$. The duration of the flight is (in $hour$):

$A$ man travels a distance of $24 \, km$ at $6 \, km/h$,another distance of $24 \, km$ at $8 \, km/h$,and a third distance of $24 \, km$ at $12 \, km/h$. His average speed for the whole journey (in $km/h$) is?

$A, B$ and $C$ can walk at the rates of $3, 4$ and $5 \text{ km/h}$ respectively. They start from Pune at $1, 2$ and $3 \text{ o'clock}$ respectively. When $B$ catches $A$,$B$ sends him back with a message to $C$. When will $C$ get the message?

$A$ train is travelling at a rate of $45 \, km/hr$. How many seconds will it take to cover a distance of $\frac{4}{5} \, km$?