If a train $110 \, m$ long passes a telegraph pole in $3 \, seconds$,then the time taken (in $seconds$) by it to cross a railway platform $165 \, m$ long is:

$A$ farmer travelled a distance of $61 \, km$ in $9 \, hrs$. He travelled partly on foot at the rate of $4 \, km/hr$ and partly on bicycle at the rate of $9 \, km/hr$. The distance travelled on foot is (in $km$):

If a boy travels from his house to school at the rate of $4 \, km/h$,he reaches the school $10 \, minutes$ earlier than the scheduled time. However,if he walks at the rate of $3 \, km/h$,he reaches $10 \, minutes$ late. Find the distance of the school from his house (in $km$).

$A$ $135\, m$ long train is running with a speed of $54\, km/h$. In what time will it pass a telegraph post? (in $seconds$)

$A, B$ and $C$ can walk at the rates of $3, 4$ and $5 \text{ km/h}$ respectively. They start from Pune at $1, 2$ and $3 \text{ o'clock}$ respectively. When $B$ catches $A$,$B$ sends him back with a message to $C$. When will $C$ get the message?

In covering a distance of $30 \, km$,Abhay takes $2 \, hours$ more than Sameer. If Abhay doubles his speed,then he would take $1 \, hour$ less than Sameer. Abhay's speed is (in $km/h$):