TWO LOCOMOTIVES APPROACH EACH OTHER ON PARALLEL TRACKS. EACH HAS A SPEED OF 95KM/H WITH RESPECT TO THE GROUNG. IF THEY ARE INITIALLY 8.5KM APART, HOW LONG WILL IT BE BEFORE THEY REACH EACH OTHER?

The distance between them decreases at a rate of 190 km/h. The time required to reduce the spacing from 8.5 km to 0 is:

8.5 km/(190 km/h)= 0.04474 h = 2.68 minutes = 2 minutes and 41 seconds

To find out how long it will take for the two locomotives to reach each other, we need to calculate the relative speed between them. Since they are approaching each other on parallel tracks, we can add their speeds to get the relative speed.

The speed of each locomotive is 95 km/h, and they are moving towards each other. Therefore, the relative speed is the sum of their speeds:

Relative speed = Speed of locomotive 1 + Speed of locomotive 2
Relative speed = 95 km/h + 95 km/h = 190 km/h

Now that we know the relative speed, we can determine how long it will take for them to cover the initial distance of 8.5 km.

Time = Distance / Speed
Time = 8.5 km / 190 km/h

To get the answer, we need to convert the units to be consistent. We can convert from km/h to hours by dividing by 60, as there are 60 minutes in an hour.

Time = (8.5 km / 190 km/h) × (1 hour / 60 minutes)
Time = (8.5 / 190) × (1 / 60) hours

Now, let's calculate the time:

Time = (8.5 / 190) × (1 / 60) hours
Time ≈ 0.007447 hours

To convert this back to minutes, we can multiply by 60:

Time ≈ 0.007447 hours × 60 minutes/hour
Time ≈ 0.44682 minutes

Therefore, it will take approximately 0.44682 minutes (or about 27 seconds) for the two locomotives to reach each other.