Two trains measuring $100\, m$ and $80\, m$ respectively,run on parallel tracks. When travelling in opposite directions,they are observed to pass each other in $9\, s$. When they are running in the same direction at the same speeds as before,the faster train passes the other in $18\, s$. Find the speeds of the two trains in $km/h$.

$A$ man covers a certain distance between his house and office on a scooter. With an average speed of $30 \, km/hr$,he is late by $10 \, min$. However,with a speed of $40 \, km/hr$,he reaches his office $5 \, min$ earlier. Find the distance between his house and office in $km$.

It takes $8\, hours$ for a $600\, km$ journey,if $120\, km$ is done by train and the rest by car. It takes $20\, minutes$ more,if $200\, km$ is done by train and the rest by car. The ratio of the speed of the train to that of the car is

$A$ $300 \, m$ long train is travelling with a speed of $45 \, km/hr$ when it passes point $A$ completely. At the same time,a motorbike starts from point $A$ with a speed of $70 \, km/hr$. When it exactly reaches the middle point of the train,the train increases its speed to $60 \, km/hr$ and the motorbike reduces its speed to $65 \, km/hr$. How much distance will the motorbike travel while passing the train completely? (in $km$)

If a person walks at $14 \, km/hr$ instead of $10 \, km/hr$,he would have walked $20 \, km$ more. The actual distance travelled by him is (in $km$)

The speed of a car increases by $2\, km/h$ after every hour. If the distance travelled in the first hour was $35\, km$,what is the total distance travelled in $12$ hours? (in $km$)