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 break down the problem:

We are given:
- The number of posts passed in 72 seconds is equal to the speed of the train (in km/h).
- We need to find the distance between the posts, \(d\), in metres.

### Step 1: Convert the speed into meters per second
Let the speed of the train be \(v\) km/h.

To convert speed from km/h to m/s:
\[
v \text{ (m/s)} = \frac{v \times 1000}{3600} = \frac{5v}{18} \text{ m/s}
\]

### Step 2: Express the total distance traveled in 72 seconds
If the train passes \(v\) posts in 72 seconds, the total distance traveled in that time is:
\[
\text{Distance traveled} = v \times d \quad \text{(where \(d\) is the distance between posts)}
\]
We can also express the distance traveled using the speed:
\[
\text{Distance traveled} = \frac{5v}{18} \times 72 \text{ meters}
\]

### Step 3: Equating both expressions for distance
Since both expressions represent the same distance, we equate them:
\[
v \times d = \frac{5v}{18} \times 72
\]

Cancel out \(v\) from both sides (assuming \(v \neq 0\)):
\[
d = \frac{5}{18} \times 72 = 20 \text{ meters}
\]

Thus, the posts are **20 meters apart**.

Would you like further details or have any questions? Here are some related questions for deeper understanding:

1. How is unit conversion used in real-world physics problems?
2. What assumptions are made in this calculation?
3. Can you derive the formula for converting km/h to m/s?
4. How would the problem change if the posts were spaced unevenly?
5. What if the speed of the train was given in m/s from the start?

**Tip:** Always ensure that units are consistent when solving problems involving speed, distance, and time.

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)?

Learn how to calculate the distance between railway posts when given the speed of a train and the time taken to pass the posts. This problem covers key algebraic concepts and unit conversion, suitable for students in Grades 9-12.

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