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### Problem Summary:
- Train 1 starts from **P** towards **Q** at 45 km/h. Distance between **P** and **Q** is 120 km.
- After 20 minutes, Train 2 starts from **Q** towards **P** at 90 km/h.
- The question asks for the distance between **P** and the meeting point **M**.

### Approach:
1. **Distance covered by Train 1 in the first 20 minutes:**
   - Speed of Train 1 = 45 km/h
   - Time = 20 minutes = \( \frac{20}{60} \) hours = \( \frac{1}{3} \) hours
   - Distance covered by Train 1 in 20 minutes = \( 45 \times \frac{1}{3} = 15 \) km

   So, Train 1 has traveled 15 km before Train 2 starts.

2. **Remaining distance between Train 1 and Train 2:**
   - Initial distance between **P** and **Q** = 120 km
   - Distance already covered by Train 1 = 15 km
   - Remaining distance between them = \( 120 - 15 = 105 \) km

3. **Relative speed of the two trains:**
   - Train 1 is moving at 45 km/h and Train 2 is moving at 90 km/h.
   - Since the trains are moving towards each other, their relative speed = \( 45 + 90 = 135 \) km/h.

4. **Time taken for the trains to meet:**
   - Time = \( \frac{\text{Remaining Distance}}{\text{Relative Speed}} = \frac{105}{135} = \frac{7}{9} \) hours.

5. **Distance traveled by Train 1 until they meet:**
   - Train 1's speed = 45 km/h
   - Time until the trains meet = \( \frac{7}{9} \) hours
   - Distance traveled by Train 1 during this time = \( 45 \times \frac{7}{9} = 35 \) km

6. **Total distance from P to M:**
   - Train 1 has already traveled 15 km in the first 20 minutes and 35 km more.
   - Total distance = \( 15 + 35 = 50 \) km

### Final Answer:
The distance between **P** and **M** is **50 km**, which is not one of the answer choices provided (400m, 550m, 350m, 450m). There may be an issue with unit conversion in the answer choices, as the result is in kilometers.

Would you like more details or further clarification?

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Here are 5 follow-up questions related to this problem:
1. How do you calculate relative speed when two objects move toward each other?
2. What if the speed of one of the trains increased? How would that change the meeting point?
3. How can you convert kilometers to meters?
4. How long will it take for Train 2 to reach Train 1 if Train 1 does not stop?
5. What happens if both trains start at the same time?

**Tip:** When trains or objects move towards each other, add their speeds to find the relative speed.

A train starts from P towards Q, which is 120 km away from P, at a speed of 45 km/h. After 20 minutes, another train starts from Q towards P at a speed of 90 km/h. If the trains meet at M, what is the distance (in km) between P and M?

Learn how to calculate the meeting point of two trains moving towards each other. This problem involves relative speed, time, and distance formulas, providing a step-by-step solution to determine the distance between point P and the meeting point M. Ideal for students in Grades 9-12.

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