Two places $A$ and $B$ are $100 \, km$ apart on a highway. One car starts from $A$ and another from $B$ at the same time. If the cars travel in the same direction at a constant speed,they meet in $5 \, hours$. If the cars travel towards each other,they meet in $1 \, hour$. What is the speed of the car running faster? (in $km/h$)

$A$ car starts with a speed of $70 \, km/h$ and its speed increases by $10 \, km/h$ every two hours. In how many hours will it cover $345 \, km$?

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 $min$):

Two persons begin together to write out a booklet containing $8190$ lines. The first person starts with the first line,writing at the rate of $200$ lines an hour; and the second person starts with the last line,then writes the $8189^{th}$ line and so on,proceeding backward at the rate of $150$ lines an hour. At what time will they meet (in $.4$)? (in hours)

$A$ 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 $km/h$):

$A$ person travels equal distances with speeds of $3 \, km/hr$,$4 \, km/hr$,and $5 \, km/hr$ and takes a total time of $47 \, minutes$. The total distance (in $km$) is: