Question

Two trains are moving towards each other with speeds 50 km/hr and 55 km/hr from different stations R and S. While they meet, the second train from station S has covered 20 km more distance than the first train which starts from station R. What is the distance between the two stations?

• A. \(400 \text{ km}\)
• B. \(440 \text{ km}\)
• C. \(460 \text{ km}\)
• D. \(420 \text{ km}\)

Hint:

In problems involving relative motion towards each other, the sum of the distances traveled by both parties equals the total distance between their starting points.

Answer 1

The Correct Option is B

Step 1: Set up the relative speed equation.
The relative speed of the trains moving towards each other is \( 50 + 55 = 105 \) km/hr.

Step 2: Calculate the distance traveled by each train when they meet.
If \( x \) is the distance covered by the train from R, then \( x + 20 \) is the distance covered by the train from S. Since they are moving towards each other, their combined distance is the total distance between the stations: \[ x + (x + 20) = 440 \] \[ 2x = 420 \] \[ x = 210 \] The total distance is \( 210 + 230 = 440 \text{ km}\).