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We are given that a train covers the distance between two stations in 45 minutes. If the train reduces its speed by 5 km/h, it takes 48 minutes to cover the same distance. We need to determine the distance between the two stations.

### Step-by-step solution:

1. **Let the speed of the train at the original speed be \( v \) km/h.**
   - The time taken is \( t_1 = 45 \) minutes = \( \frac{45}{60} = 0.75 \) hours.

   Using the formula for distance:
   \[
   d = v \times t_1 = v \times 0.75
   \]
   where \( d \) is the distance between the two stations.

2. **When the speed is reduced by 5 km/h:**
   - The new speed is \( v - 5 \) km/h.
   - The time taken is \( t_2 = 48 \) minutes = \( \frac{48}{60} = 0.8 \) hours.

   The distance remains the same:
   \[
   d = (v - 5) \times 0.8
   \]

3. **Set the two distance expressions equal:**
   Since the distance is the same, we can set the two equations for \( d \) equal to each other:
   \[
   v \times 0.75 = (v - 5) \times 0.8
   \]

4. **Solve for \( v \):**
   Expand the equation:
   \[
   0.75v = 0.8(v - 5)
   \]
   \[
   0.75v = 0.8v - 4
   \]
   Bring the terms involving \( v \) on one side:
   \[
   0.75v - 0.8v = -4
   \]
   \[
   -0.05v = -4
   \]
   \[
   v = \frac{-4}{-0.05} = 80 \, \text{km/h}
   \]

5. **Calculate the distance:**
   Now that we know the speed \( v = 80 \, \text{km/h} \), substitute into the formula for distance:
   \[
   d = v \times t_1 = 80 \times 0.75 = 60 \, \text{km}
   \]

### Conclusion:
The distance between the two stations is **60 km**.

Would you like more details on any step or have further questions?

Here are some related questions:
1. What would happen to the time taken if the train increased its speed by 10 km/h?
2. How would the formula change if the time was given in seconds instead of minutes?
3. Can this method be used if the train's speed reduction is in percentage instead of km/h?
4. How would the result differ if the time taken was measured in kilometers instead of hours?
5. What would the impact be if the train accelerated at a constant rate over the distance?

**Tip:** Always ensure to convert time units to hours when dealing with speed in km/h to keep units consistent.

A train covers the distance between two stations in 45 minutes, if the train reduces its speed by 5 km/h it covers the same distance in 48 minutes. So what will be the distance between those two stations?

Learn how to calculate the distance between two stations when a train reduces its speed. The problem involves key algebraic concepts such as distance-speed-time relationships and solving linear equations. Suitable for students in Grades 9-10.

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