Train A crosses a pole in 16 seconds and a platform 200 meters long in 24 seconds. Calculate the time taken by train A to cross another train B, which is 480 meters long and moving in the opposite direction at a speed of 108 km/h.

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**Solution:**

1. First, find the speed of train A.
   - Let the length of train A be *L* meters.
   - Time to cross a pole = 16 seconds, so speed of train A = $ $\frac{L}{16}$ $ m/s.

2. Time to cross a platform of 200 meters = 24 seconds.
   - Distance covered while crossing platform = length of train + length of platform = $ L + 200 $ meters.
   - Speed = $ $\frac{L + 200}{24}$ $ m/s.

3. Since speed is constant, equate the two expressions:
   $$
   $\frac{L}{16} = \frac{L + 200}{24}$
   $$

4. Cross-multiplied:
   $$
   24L = 16(L + 200)
   $$
   $$
   24L = 16L + 3200
   $$
   $$
   24L - 16L = 3200
   $$
   $$
   $8L = 3200 \implies L = 400 \text{ meters}$
   $$

5. Speed of train A:
   $$
   = $\frac{400}{16} = 25 \text{ m/s}$
   $$

6. Speed of train B is given as 108 km/h.
   Convert to m/s:
   $$
   $108 \times \frac{5}{18} = 30 \text{ m/s}$
   $$

7. Since trains move in opposite directions, their relative speed = 25 + 30 = 55 m/s.

8. Total length to be crossed = length of train A + length of train B = 400 + 480 = 880 meters.

9. Time taken to cross each other:
   $$
   = $\frac{880}{55} = 16 \text{ seconds}$
   $$

**Answer:** 16 seconds

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