How many seconds will a train $60 \; m$ in length,travelling at the rate of $42 \; km/h$,take to pass another train $84 \; m$ long,proceeding in the same direction at the rate of $30 \; km/h$?

$A$ $270 \;m$ long train running at a speed of $120 \;km/hr$ crosses another train running in the opposite direction at a speed of $80 \;km/hr$ in $9 \;seconds$. What is the length (in $m$) of the other train?

$A$ train moves past a telegraph post and a bridge $264 \; m$ long in $8 \; seconds$ and $20 \; seconds$ respectively. What is the speed of the train (in $km/hr$)?

How many seconds will a $500 \;m$ long train take to cross a man walking with a speed of $3 \;km/h$ in the same direction as the moving train,if the speed of the train is $63 \;km/h$?

Two trains are running at $40 \; km/hr$ and $20 \; km/hr$ respectively in the same direction. The faster train completely passes a man in the slower train in $5 \; seconds$. What is the length (in $m$) of the faster train?

$A$ jogger running at $9 \; km/hr$ alongside a railway track is $240 \; m$ ahead of the engine of a $120 \; m$ long train running at $45 \; km/hr$ in the same direction. In how much time (in $sec$) will the train pass the jogger?