Let's solve this step-by-step.
1. Determine the Speed Ratio:
The speed ratio of train A to train B is given as 4:3. This means:
- Speed of train A = 4x
- Speed of train B = 3x
2. Calculate the Total Speed when Crossing Each Other:
When trains A and B cross each other while traveling in opposite directions, their relative speed is the sum of their individual speeds:
- Total speed = 4x + 3x = 7x
3. Find the Distance Covered when Crossing Each Other:
When crossing each other in 18 seconds, the total distance covered by both trains combined is the total speed multiplied by the time:
- Distance = (total speed) × (time)
- Distance = 7x × 18 = 126x
4. Distance Covered by Train A when Crossing a Pole:
When train A crosses a pole in 24 seconds, the distance it covers is:
- Distance = (speed of train A) × (time)
- Distance = 4x × 24 = 96x
5. Time Taken by Train B to Cross the Same Distance:
We need to find the time taken by train B to cross a distance of 96x. Since speed of train B is 3x, we use the relation:
- Time = (distance) / (speed of train B)
- Time = (96x) / (3x) = 32 seconds
Therefore, the time taken by train B to cross a pole is 32 seconds.
