$A$ 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 $km/h$)

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 $\text{km}$):

$A$ car starts with a speed of $70 \, km/h$ and its speed increases by $10 \, km/h$ every two hours. In how many hours will it cover $345 \, km$?

$A$ train,when moving at an average speed of $40 \, km/hr$,reaches its destination on time. When its average speed becomes $35 \, km/hr$,it reaches its destination $15 \, minutes$ late. Find the length of the journey in $km$.

$A$ car driver leaves Bangalore at $8:30 \, am$ and expects to reach a place $300 \, km$ from Bangalore at $12:30 \, pm$. At $10:30 \, am$, he finds that he has covered only $40 \%$ of the distance. By how much does he have to increase the speed of the car in order to keep up with his schedule? (in $km/h$)

Starting from his house,a student walks at a speed of $2.5 \, km/hr$ and reaches his school $6 \, minutes$ late. Next day he increases his speed by $1 \, km/hr$ and reaches the school $6 \, minutes$ early. How far is the school from his house? (in $km$)