Two trains A and B have lengths of $400 ext{ m}$ and $(400 + x) ext{ m}$ respectively, and both move at the same speed. Train A crosses a pole in $16$ seconds, while train B crosses the same pole in $24$ seconds. How long will train B take to cross a platform that is $400 ext{ m}$ long?

Question

Two trains A and B have lengths of $400 	ext{ m}$ and $(400 + x) 	ext{ m}$ respectively, and both move at the same speed. Train A crosses a pole in $16$ seconds, while train B crosses the same pole in $24$ seconds. How long will train B take to cross a platform that is $400 	ext{ m}$ long?

Accepted Answer

**Solution:**

1. Calculate the speed of train A:
   - Length of train A = $400 	ext{ m}$
   - Time taken to cross pole = $16 	ext{ sec}$
   - Speed = $\frac{	ext{Distance}}{	ext{Time}} = \frac{400}{16} = 25 	ext{ m/sec}$

2. Since both trains move at the same speed, speed of train B is also $25 	ext{ m/sec}$.

3. Using train B's crossing time for the pole:
   - Length of train B = $400 + x$
   - Time to cross pole = $24 	ext{ sec}$
   - Speed = $25 = \frac{400 + x}{24}$

4. Solve for $x$:
   $$400 + x = 25 	imes 24 = 600$$
   $$x = 600 - 400 = 200 	ext{ m}$$

5. Now, find the time taken by train B to cross a platform of length $400 	ext{ m}$:
   - Total distance to cross = Length of train B + Length of platform = $600 + 400 = 1000 	ext{ m}$
   - Time = $\frac{1000}{25} = 40 	ext{ sec}$

**Answer:** $40 	ext{ sec}$

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