A car and a bus are travelling towards each other.
They are 510 km apart at 1320 hours and they pass each other at 1620 hours. If the car is travelling at a speed of 90 km/h, find the speed of the bus.

To solve this problem, we need to determine the speed of the bus given the time they meet and the speed of the car.

### Step-by-Step Solution:

1. **Calculate the time taken for the car and the bus to meet:**

   They pass each other at 1620 hours, starting from 1320 hours. The time difference is:
   \[
   1620 \, \text{hours} - 1320 \, \text{hours} = 4 \, \text{hours}
   \]

2. **Calculate the distance covered by the car in 4 hours:**

   The car is travelling at a speed of 90 km/h. Therefore, the distance covered by the car in 4 hours is:
   \[
   \text{Distance}_{\text{car}} = \text{Speed}_{\text{car}} \times \text{Time} = 90 \, \text{km/h} \times 4 \, \text{hours} = 360 \, \text{km}
   \]

3. **Determine the remaining distance covered by the bus:**

   The total distance between the car and the bus was 510 km. The remaining distance, which is the distance covered by the bus, is:
   \[
   \text{Distance}_{\text{bus}} = 510 \, \text{km} - 360 \, \text{km} = 150 \, \text{km}
   \]

4. **Calculate the speed of the bus:**

   The bus also travels for 4 hours (since they meet after 4 hours). Therefore, the speed of the bus is:
   \[
   \text{Speed}_{\text{bus}} = \frac{\text{Distance}_{\text{bus}}}{\text{Time}} = \frac{150 \, \text{km}}{4 \, \text{hours}} = 37.5 \, \text{km/h}
   \]

### Conclusion:

The speed of the bus is \(37.5 \, \text{km/h}\).

Would you like details or have any questions? Here are 5 questions you can ask next:
1. How to solve problems involving relative speed?
2. Can you explain more about time-distance-speed relationships?
3. What are some other examples of relative motion problems?
4. How to deal with problems involving different units of speed and distance?
5. Can you solve a problem involving three moving objects?

**Tip:** Always ensure units are consistent when solving motion problems to avoid calculation errors.

Learn how to solve a speed, distance, and time problem involving a car and a bus. Calculate the speed of the bus given that they start 510 km apart at 1320 hours and meet at 1620 hours. Detailed step-by-step solution included. Suitable for students in Grades 7-9.

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