Sound travels $330 \text{ m/s}$. If the sound of a thundercloud is heard $10 \text{ s}$ after the flash,the distance of the thundercloud is (in $\text{km}$):

$A$ and $B$ run a kilometer and $A$ wins by $25 \text{ sec}$. $A$ and $C$ run a kilometer and $A$ wins by $275 \text{ m}$. When $B$ and $C$ run the same distance,$B$ wins by $30 \text{ sec}$. The time taken by $A$ to run a kilometer is

$A$ 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 travels $225 \ km$ in $3.5 \ hours$ and $370 \ km$ in $5 \ hours.$ Find out the average speed of the train in $km/h$.

$A$ goods train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in $60 \, s$. Whereas a passenger on the passenger train marks that he crossed the goods train in $40 \, s$. If the speeds of the trains are in the ratio of $1:2$,find the ratio of their lengths.

Two trains,each of length $90\, m,$ run on parallel tracks. When running in the same direction,the faster train passes the slower train completely in $18\, s,$ but when they are running in opposite directions approaching each other at the same speeds as before,they cross each other in $9\, s.$ Find the speed of each train (in $m/s$).