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 \( d \) be the distance between the posts in meters, and let the speed of the train be \( v \) in kilometers per hour. 

We know two things:
1. The number of posts passed in 72 seconds is the same as the speed of the train in km/h.
2. The distance traveled by the train in 72 seconds is the product of its speed and time.

### Step 1: Convert the speed to meters per second
Speed \( v \) in km/h can be converted to meters per second using the formula:

\[
v_{\text{m/s}} = \frac{v_{\text{km/h}} \times 1000}{3600} = \frac{v}{3.6}
\]

### Step 2: Calculate the distance traveled in 72 seconds
The distance traveled in 72 seconds is:

\[
\text{Distance} = v_{\text{m/s}} \times 72 = \frac{v}{3.6} \times 72 = 20v
\]

### Step 3: Relating the number of posts to the speed
Since the number of posts passed is equal to the speed of the train, the total number of posts passed in 72 seconds is \( v \). Thus, the distance traveled, \( 20v \), must also equal the distance between \( v \) posts, which is \( v \times d \), where \( d \) is the distance between the posts:

\[
20v = v \times d
\]

### Step 4: Solve for \( d \)
By dividing both sides by \( v \):

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

Thus, the distance between the posts is 20 meters.

---

Would you like a deeper explanation, or do you have any questions?

Here are five related questions to extend this topic:
1. What if the speed of the train were doubled? How would that affect the number of posts passed?
2. How would the problem change if the posts were not equally spaced?
3. How can you convert units like km/h to m/s for other problems?
4. What assumptions are made in this problem about the train's motion?
5. How can you calculate the total distance traveled in a different time frame?

**Tip:** Always make sure to convert units consistently when working with speed, distance, and time calculations.

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 the number of posts passed in 72 seconds equals the speed of the train in km/h. This problem involves key concepts in speed, distance, and unit conversion, suitable for Grades 9-10.

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