$A$ man covers a certain distance between his house and office on a scooter. With an average speed of $30 \, km/hr$,he is late by $10 \, min$. However,with a speed of $40 \, km/hr$,he reaches his office $5 \, min$ earlier. Find the distance between his house and office in $km$.

$A$ speed of $45\, km/h$ is equivalent to which speed in $m/s$?

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 $B$?

$A$ 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 $km/h$)

Two trains,$130 \,m$ and $110 \,m$ long,are moving in the same direction. The faster train takes $1 \,minute$ to pass the other completely. If they are moving in opposite directions,they pass each other completely in $3 \,seconds$. Find the speed of each train (in $m/s$).

Two guns were fired from the same place at an interval of $13 \text{ minutes}$,but a person in a train approaching the place hears the second shot $12 \text{ minutes } 30 \text{ seconds}$ after the first. Find the speed of the train,assuming that sound travels at $330 \text{ m/s}$ (in $\text{km/hr}$).