When two train of length 100 metre and 95 metre respectively run in same direction, then cross each other in 27 sec. and while running in opposite direction, they cross in 9 sec. Accordingly, what is the speed of trains ?

Options

A. 44 km./hour, 22 km./hour
B. 52 km./hour, 26 km./hour
C. 36 km./hour, 18 km./hour
D. 40 km./hour, 20 km./hour

Answer

To solve the problem, we need to find the speeds of the two trains based on the information given about their lengths and the time taken to cross each other in both the same and opposite directions.

**Step 1: Understand the lengths of the trains.**
- Train A length = 100 meters
- Train B length = 95 meters

**Hint:** Remember that the total distance covered when two trains cross each other is the sum of their lengths.

**Step 2: Calculate the total distance when trains cross each other in the same direction.**
- Total distance = Length of Train A + Length of Train B
- Total distance = 100 m + 95 m = 195 m

**Hint:** When trains are moving in the same direction, the distance they need to cover to completely cross each other is the sum of their lengths.

**Step 3: Calculate the relative speed when trains cross each other in the same direction.**
- Time taken to cross = 27 seconds
- Relative speed = Total distance / Time taken
- Relative speed = 195 m / 27 s = 7.22 m/s (approximately)

**Hint:** The relative speed in the same direction is the difference of their speeds.

**Step 4: Set up the equation for speeds when trains are moving in the same direction.**
- Let speed of Train A = v_A (m/s)
- Let speed of Train B = v_B (m/s)
- Then, v_A - v_B = 7.22 m/s

**Hint:** The relative speed when moving in the same direction is the difference of their speeds.

**Step 5: Calculate the total distance when trains cross each other in the opposite direction.**
- Total distance = Length of Train A + Length of Train B = 195 m (same as before)

**Hint:** When trains are moving in opposite directions, the distance they need to cover is still the sum of their lengths.

**Step 6: Calculate the relative speed when trains cross each other in the opposite direction.**
- Time taken to cross = 9 seconds
- Relative speed = Total distance / Time taken
- Relative speed = 195 m / 9 s = 21.67 m/s (approximately)

**Hint:** The relative speed in the opposite direction is the sum of their speeds.

**Step 7: Set up the equation for speeds when trains are moving in opposite directions.**
- From the previous step, we have:
- v_A + v_B = 21.67 m/s

**Hint:** The relative speed when moving in opposite directions is the sum of their speeds.

**Step 8: Solve the system of equations.**
- We have two equations:
1. v_A - v_B = 7.22
2. v_A + v_B = 21.67

**Step 9: Add the two equations to eliminate v_B.**
- (v_A - v_B) + (v_A + v_B) = 7.22 + 21.67
- 2v_A = 28.89
- v_A = 28.89 / 2 = 14.445 m/s (approximately)

**Hint:** When you add the equations, the v_B terms cancel out.

**Step 10: Substitute v_A back to find v_B.**
- Using v_A in one of the equations:
- v_A - v_B = 7.22
- 14.445 - v_B = 7.22
- v_B = 14.445 - 7.22 = 7.225 m/s (approximately)

**Hint:** Substitute the value of v_A into one of the original equations to find v_B.

**Final Answer:**
- Speed of Train A = 14.445 m/s (approximately)
- Speed of Train B = 7.225 m/s (approximately)