Two trains are running on parallel tracks in the same direction. The faster train crosses a man standing in the slower train in 30 seconds. If the speed of the faster train is $18 ext{ km/h}$ more than the slower train, find the length of the faster train in meters.

Question

Two trains are running on parallel tracks in the same direction. The faster train crosses a man standing in the slower train in 30 seconds. If the speed of the faster train is $18 	ext{ km/h}$ more than the slower train, find the length of the faster train in meters.

Accepted Answer

**Solution:**

1. Let the speed of the slower train be $x 	ext{ km/h}$. Then the speed of the faster train is $(x + 18) 	ext{ km/h}$.

2. Since both trains are moving in the same direction, the relative speed of the faster train with respect to the slower train is:
   $$ (x + 18) - x = 18 	ext{ km/h} $$

3. Convert the relative speed from km/h to m/s:
   $$ 18 	imes \frac{5}{18} = 5 	ext{ m/s} $$

4. The faster train crosses a man standing in the slower train in 30 seconds. The distance covered in this time is the length of the faster train, say $L$ meters.

5. Using the formula:
   $$ 	ext{Distance} = 	ext{Speed} 	imes 	ext{Time} $$
   $$ L = 5 	imes 30 = 150 	ext{ meters} $$

**Answer:** $150$ meters

Answer

Answer

Answer

Answer