One of the two buses completes a journey of $300 \, km$ in $7 \frac{1}{2} \, hours$ and the other a journey of $450 \, km$ in $9 \, hours.$ The ratio of their average speed is:

$A$ person has to reach a certain place at a certain time. He finds that he will be $15 \text{ minutes}$ late if he walks at $4 \text{ km/h}$,and $10 \text{ minutes}$ earlier if he walks at $6 \text{ km/h}$. How far has he to walk? (in $\text{km}$)

$A$ passenger train running at the speed of $80 \text{ km/h}$ leaves the railway station $6 \text{ hours}$ after a goods train leaves and overtakes it in $4 \text{ hours}$. What is the speed of the goods train? (in $\text{km/h}$)

$A$ dog finds a cat at $25$ leaps away. The cat sees the dog coming towards it and starts running with the dog in hot pursuit. In every minute, the dog makes $5$ leaps and the cat makes $6$ leaps, and one leap of the dog is equal to $2$ leaps of the cat. Find the time in which the dog will catch the cat (in minutes).

$A$ train $50\, m$ long passes a platform $100\, m$ long in $10\, s$. The speed of the train in $m/s$ is:

$A$ 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 $60 \text{ km/h}$?