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?

The distance between places $A$ and $B$ is $999 \, km$. An express train leaves place $A$ at $6 \, am$ and runs at a speed of $55.5 \, km/h$. The train stops on the way for $1 \, hr \, 20 \, min$. It reaches $B$ at?

$A$ student goes to school at the rate of $2 \frac{1}{2} \text{ km/h}$ and reaches $6 \text{ min}$ late. If he travels at the speed of $3 \text{ km/h}$,he is $10 \text{ min}$ early. The distance (in $\text{km}$) between the school and his house is:

The distance between two stations,Delhi and Amritsar,is $450 \, km$. $A$ train starts at $4 \, p.m.$ from Delhi and moves towards Amritsar at an average speed of $60 \, km/hr$. Another train starts from Amritsar at $3:20 \, p.m.$ and moves towards Delhi at an average speed of $80 \, km/hr$. At what time will the two trains meet?

$A$ man starts running from point $P$ at $11:00$ $a.m.$ with a speed of $10 \, km/hr$. He runs for $2 \, hours$ and then takes a $1 \, hour$ rest. He continues this pattern until he is caught by another man who starts at $2:00 \, p.m.$ from point $P$ and runs non-stop at a speed of $15 \, km/hr$ toward the first man. At what time (in $p.m.$) will the first man be caught?

$A$ student walks from his house at a speed of $2 \frac{1}{2} \text{ km/h}$ and reaches his school $6 \text{ min}$ late. The next day,he increases his speed by $1 \text{ km/h}$ and reaches $6 \text{ min}$ before school time. How far is the school from his house? (in $\text{km}$)