A car travels 180 km in 6 hours and a bus travels 315 km in 9 hours at uniform speeds. Find the ratio of distance travelled by car to bus in one hour.

Options

A. `7:6`
B. `5:8`
C. `8:5`
D. `6:7`

Answer

To solve the problem, we need to find the distance traveled by both the car and the bus in one hour and then determine the ratio of these distances.

### Step-by-Step Solution:

1. **Calculate the speed of the car:**
- The car travels 180 km in 6 hours.
- Speed of the car = Total distance / Total time
- Speed of the car = 180 km / 6 hours = 30 km/h

2. **Calculate the speed of the bus:**
- The bus travels 315 km in 9 hours.
- Speed of the bus = Total distance / Total time
- Speed of the bus = 315 km / 9 hours = 35 km/h

3. **Set up the ratio of distances traveled in one hour:**
- Distance traveled by car in one hour = 30 km
- Distance traveled by bus in one hour = 35 km
- Ratio of distance traveled by car to distance traveled by bus = Distance by car : Distance by bus
- Ratio = 30 km : 35 km

4. **Simplify the ratio:**
- To simplify, we can divide both numbers by their greatest common divisor (GCD), which is 5.
- 30 ÷ 5 = 6
- 35 ÷ 5 = 7
- Therefore, the simplified ratio is 6 : 7.

### Final Answer:
The ratio of the distance traveled by the car to the bus in one hour is **6 : 7**.