A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

To find the speed of the train, we need to apply the basic formula of speed:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

1. **When the train moves past a telegraph post**, the distance it covers is equal to the length of the train. The time taken is 8 seconds. Let the length of the train be \( L \).

2. **When the train moves past a bridge 264 m long**, the total distance it covers is the length of the train plus the length of the bridge, i.e., \( L + 264 \) meters. The time taken for this is 20 seconds.

### Step 1: Find the length of the train
- For the telegraph post:
  \[
  \text{Speed} = \frac{L}{8}
  \]

- For the bridge:
  \[
  \text{Speed} = \frac{L + 264}{20}
  \]

Since the speed of the train is constant, the two speeds must be equal:

\[
\frac{L}{8} = \frac{L + 264}{20}
\]

### Step 2: Solve for \( L \)
Cross-multiply to eliminate the fractions:

\[
20L = 8(L + 264)
\]

Expanding the equation:

\[
20L = 8L + 2112
\]

Subtract \( 8L \) from both sides:

\[
12L = 2112
\]

Now, divide by 12:

\[
L = \frac{2112}{12} = 176 \, \text{m}
\]

So, the length of the train is 176 meters.

### Step 3: Find the speed of the train
Now that we know the length of the train is 176 meters, we can find the speed:

Using the formula for speed when the train passes the telegraph post:

\[
\text{Speed} = \frac{L}{8} = \frac{176}{8} = 22 \, \text{m/s}
\]

Thus, the speed of the train is **22 meters per second**.

Would you like more details or have any questions?

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Here are some related questions for further practice:
1. How long will the train take to cross a platform that is 350 m long?
2. What would be the speed of the train if it crossed the telegraph post in 6 seconds?
3. If the length of the train increased by 10%, how would that affect the time to cross the bridge?
4. What is the time taken for the train to cover 1 km at this speed?
5. How would the speed change if the train crossed a longer bridge in 25 seconds?

**Tip:** For problems involving motion, always start with identifying known quantities (distance and time) and use the basic speed formula.

Learn how to calculate the speed of a train moving past a telegraph post and a 264 m long bridge. Understand key concepts of speed, distance, and time, and follow a step-by-step solution to solve for the train's speed. Suitable for students in Grades 8-10.

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