$A$ train speeds past a pole in $15 \, \text{seconds}$ and speeds past a $100 \, \text{meters}$ long platform in $25 \, \text{seconds}$. Its length in meters is:

Two men are standing on opposite ends of a bridge of $1200 \, m$ long. If they walk towards each other at the rate of $5 \, m/min$ and $10 \, m/min$ respectively,in how much time will they meet each other? (in $minutes$)

$A$ train starts from Delhi on Sunday at $9 \, am$ with a speed of $25 \, km/h$. Another train starts from the same place on the same day at $3 \, pm$ with a speed of $40 \, km/h$ in the same direction. Find at what distance from Delhi both trains will meet? (in $km$)

$A$ boy goes to his school from his house at a speed of $3 \, km/hr$ and returns at a speed of $2 \, km/hr$. If he takes $5 \, hours$ in total for the round trip,the distance between his house and school is (in $km$):

$A$ train travelling with a speed of $60 \, km/h$ catches another train travelling in the same direction and then leaves it $120 \, m$ behind in $18 \, seconds$. The speed of the second train is (in $km/h$):

If a man walks at the rate of $5\, km/h$,he misses a train by $7\, minutes$. However,if he walks at the rate of $6\, km/h$,he reaches the station $5\, minutes$ before the arrival of the train. The distance covered by him to reach the station is (in $km$)