Problems on Trains question bank (Quantitative Aptitude)

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 $30 \; km/h$?

Two trains running at the rate of $45 \; km/h$ and $36 \; km/h$ respectively,on parallel tracks in opposite directions,are observed to pass each other in $8 \; seconds$. When they are running in the same direction at the same rate as before,a person sitting in the faster train observes that he passes the other in $30 \; seconds$. Find the length of the trains (in $m$).