The jogging track in a sports complex is $726 \, m$ in circumference. Deepak and his wife start from the same point and walk in opposite directions at $4.5 \, km/h$ and $3.75 \, km/h$ respectively. They will meet for the first time in (in $min$):

$A$ thief is spotted by a policeman from a distance of $400\, m$. When the policeman starts the chase,the thief also starts running. Assuming the speed of the thief is $5\, km/h$ and that of the policeman is $9\, km/h$,how far will the thief have run before he is overtaken by the policeman? (in $m$)

$A$ motorcyclist left $6 \frac{2}{3}$ minutes later than the scheduled time,but in order to reach his destination $21 \, km$ away on time,he had to increase his speed by $12 \, km/h$ from his usual speed. What is the usual speed (in $km/h$) of the motorcyclist?

Rakesh sets out to cycle from Delhi to Mathura and at the same time Suresh starts from Mathura to Delhi. After passing each other,they complete their journeys in $9$ and $16 \, \text{hours}$,respectively. At what speed does Suresh cycle if Rakesh cycles at $16 \, \text{km/h}$?

$A$ goods train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in $60 \, s$. Whereas a passenger on the passenger train marks that he crossed the goods train in $40 \, s$. If the speeds of the trains are in the ratio of $1:2$,find the ratio of their lengths.

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 $m$).