An automobile traveling 95 km/h overtakes a 1.00km long train travelling in the same direction on a track parallel to the road. if the train's speed is 75km/h, how long does it take the car to pass it and how far will the car have traveled in this time? what are the results if the car and train are traveling in opposite directions?

Lovely.

The car is traveling at 95 km/h, and the train is at 75 km/h.

Remember the train is 1 km long.

a)

With respect to the train the car is not moving as much as 75 km/h.

The car with respect to the train is moving as much as 95 - 75 = 20 km/h

Recall the train is 1 km long.

Time to cover the 1km long train = Distance / speed = 1 / 20 = (1/20) hour.

= (1/20)*60 minutes = 3 minutes.

So the car would pass the train in 3 minutes.    

b)

Now if they are traveling in opposite directions;

the car with respect to the train = 75 + 95 = 170 km/h

Time to cover the 1km long train = Distance / speed = 1 / 170 = (1/170) hour.

= (1/170)*60 minutes = (6/17) minutes 

= (6/17)*60 seconds = 360/17 seconds ≈ 21.176 seconds.

The velocity difference between the car and train is 20km/h.
t=(1km)/(20km/h)=0,05h t=3 minutes.

when the opposite direction.
The velocity difference is 170km/h.

t=(1km)/(170km/h)=5,88*10^-3 h t=21,17 seconds.