$A$ student goes to school at the rate of $2 \frac{1}{2} \text{ km/h}$ and reaches $6 \text{ min}$ late. If he travels at the speed of $3 \text{ km/h}$,he is $10 \text{ min}$ early. The distance (in $\text{km}$) between the school and his house is:

Two trains are moving in the same direction at $50 \, km/h$ and $30 \, km/h$. The faster train crosses a man in the slower train in $18 \, seconds$. Find the length of the faster train (in $m$).

Excluding stoppages, the speed of a bus is $54 \, km/h$ and including stoppages, it is $45 \, km/h$. For how many minutes does the bus stop per hour?

$A$ train $150 \, m$ long takes $20 \, s$ to cross a platform $450 \, m$ long. The speed of the train in $km/h$ is:

Two trains start at the same time from two stations and proceed towards each other at the speeds of $20 \, km/h$ and $25 \, km/h$ respectively. When they meet,it is found that one train has travelled $80 \, km$ more than the other. Find the distance between the two stations (in $km$).

$A$ starts from a place $P$ to go to a place $Q$. At the same time $B$ starts from $Q$ to $P$. If after meeting each other $A$ and $B$ took $16$ and $25$ $hours$ more respectively to reach their destinations,the ratio of their speeds is