$A$ car starts from $A$ for $B$ travelling at $20 \, km/h$. $1 \frac{1}{2} \, hours$ later,another car starts from $A$ and,travelling at the rate of $30 \, km/h$,reaches $B$ $2 \frac{1}{2} \, hours$ before the first car. Find the distance from $A$ to $B$ (in $km$).

$A$ train $300 \text{ m}$ long is running at a speed of $90 \text{ km/h}$. How many seconds will it take to cross a $200 \text{ m}$ long train running in the opposite direction at a speed of $60 \text{ km/h}$?

Car $A$ runs at the speed of $65 \text{ km/h}$ and reaches its destination in $8 \text{ hours}$. Car $B$ runs at the speed of $70 \text{ km/h}$ and reaches its destination in $4 \text{ hours}$. What is the respective ratio of distances covered by Car $A$ and Car $B$?

$A$ car travels from $P$ to $Q$ at a constant speed. If its speed were increased by $10 \, km/h$,it would have taken $1 \, hour$ less to cover the distance. It would have taken a further $45 \, minutes$ less if the speed was increased by another $10 \, km/h$. The distance between the two cities is (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 $km/hr$):

$A$ bullock cart has to cover a distance of $80 \text{ km}$ in $10 \text{ hours}$. If it covers half of the journey in $\frac{3}{5}$ of the total time,what should be its speed to cover the remaining distance in the time left? (in $\text{km/h}$)