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 $m$).

$A$ $180\, m$ long train crosses another $270\, m$ long train running in the opposite direction in $10.8\, seconds$. If the speed of the first train is $60\, km/h$, what is the speed of the second train in $km/h$?

$A$ boy walking at a speed of $10\, km/hr$ reaches his school $15\, minutes$ late. Next time he increases his speed by $2\, km/hr$, but still he is late by $5\, minutes$. Find the distance of his school from his house (in $km$).

The ratio of the speeds of a car,a train,and a bus is $5:9:4$. The average speed of the car,the bus,and the train together is $72 \text{ km/h}$. What is the average speed of the car and the train together? (in $\text{km/h}$)

$A$ man travelled from the village to the post office at the rate of $25 \, km/hr$ and walked back at the rate of $4 \, km/hr$. If the whole journey took $5 \, hours \, 48 \, minutes$,find the distance of the post office from the village (in $km$).

$A$ person travels from $P$ to $Q$ at a speed of $40 \, km/hr$ and returns by increasing his speed by $50 \%$. What is his average speed for both the trips? (in $km/hr$)