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 find the speed of the bus, we first need to determine the total time it takes for the car and the bus to meet. The car and the bus start 510 km apart at 1320 hours and pass each other at 1620 hours.

First, calculate the total time in hours from 1320 hours to 1620 hours:

\[
1620 \text{ hours} - 1320 \text{ hours} = 3 \text{ hours}
\]

Next, determine the distance the car travels in those 3 hours. Given the speed of the car is 90 km/h, we use the formula:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

So, the distance traveled by the car in 3 hours is:

\[
90 \text{ km/h} \times 3 \text{ hours} = 270 \text{ km}
\]

Since the total distance between the car and the bus is 510 km and the car travels 270 km of that distance, the remaining distance traveled by the bus is:

\[
510 \text{ km} - 270 \text{ km} = 240 \text{ km}
\]

Now, to find the speed of the bus, we use the formula for speed:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

The bus travels 240 km in the same 3 hours, so the speed of the bus is:

\[
\text{Speed of the bus} = \frac{240 \text{ km}}{3 \text{ hours}} = 80 \text{ km/h}
\]

Therefore, the speed of the bus is \(80 \text{ km/h}\).

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you calculate the average speed of a round trip if the speeds are different on each leg?
2. What is the relative speed of two objects moving towards each other?
3. How do you solve problems involving distance, speed, and time for multiple objects?
4. What happens to the time taken if the speed of one object is doubled?
5. How do you approach problems where objects start at different times but meet at a common point?

**Tip:** When solving distance-speed-time problems, always make sure to keep your units consistent (e.g., kilometers and hours) to avoid calculation errors.

Learn how to solve a distance, speed, and time problem involving a car and a bus meeting on a road. Understand how to calculate the speed of the bus when given the speed of the car and their meeting time. Suitable for students in Grades 7-9.

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