The posts supporting overhead wires on a railway are equally-spaced while travelling on a train I notice that the number of posts passed in 72 seconds is the same as the speed of the train ( in km per hour ) how far apart are the posts ( in metres)?

Let's solve this step by step.

### Given:
- The number of posts passed in 72 seconds equals the speed of the train in kilometers per hour (km/h).
- We need to find the distance between the posts in meters.

### Let:
- \( v \) be the speed of the train in km/h.
- \( d \) be the distance between the posts in meters.

### Step 1: Relationship between speed and number of posts

In 72 seconds, the train travels a distance equal to the number of posts passed multiplied by the distance between the posts.

Since the number of posts passed in 72 seconds is equal to the train's speed in km/h, we have:

\[ \text{Number of posts passed} = \frac{\text{Distance traveled in 72 seconds (in meters)}}{d} \]

But we also know that this number is equal to the speed \( v \) in km/h.

### Step 2: Convert the speed to meters per second

1 km/h = \(\frac{1000 \text{ meters}}{3600 \text{ seconds}}\)

So the speed \( v \) in meters per second is:

\[ v_{\text{m/s}} = \frac{v \times 1000}{3600} = \frac{5v}{18} \text{ m/s} \]

### Step 3: Calculate the distance traveled in 72 seconds

Distance traveled in 72 seconds:

\[ \text{Distance} = v_{\text{m/s}} \times 72 = \frac{5v}{18} \times 72 = 20v \text{ meters} \]

### Step 4: Set up the equation for the number of posts

The number of posts passed \( n \) is:

\[ n = \frac{20v}{d} \]

But \( n \) is also equal to \( v \) (since the problem states that the number of posts passed is the same as the speed in km/h).

So:

\[ v = \frac{20v}{d} \]

### Step 5: Solve for \( d \)

Cancel \( v \) from both sides (assuming \( v \neq 0 \)):

\[ 1 = \frac{20}{d} \]

So:

\[ d = 20 \text{ meters} \]

### Final Answer:

The posts are **20 meters apart**.

Would you like more details or have any questions?

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Here are 5 related questions to expand on this topic:

1. If the speed of the train doubled, how would that affect the distance between the posts?
2. How long would it take the train to pass 50 posts at the same speed?
3. What if the posts were 15 meters apart? How would the number of posts passed in 72 seconds change?
4. If the train's speed was 90 km/h, how far would it travel in 1 minute?
5. How would the number of posts passed in 72 seconds change if the speed decreased by 20%?

**Tip:** When solving problems involving speed and time, converting units to a consistent system (e.g., meters and seconds) simplifies the calculations.

Explore how to calculate the distance between equally-spaced railway posts based on the speed of a train passing them. Step-by-step solution provided, including conversions from km/h to m/s. Suitable for Grades 7-9 students.

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