Please read the question carefully and answer the questions carefully

The ratio between the speed of a train and a car is 12 : 11 respectively. Also, a bus covered a distance of 315 kms in 7 hours. The speed of the bus is three-fourth the speed of the train. How much distance will the car cover in 6 hours ?

Options

480 km

Cannot be determined

450 km

330 km

Let's solve this step by step.

### Step 1: Determine the speed of the bus.
- The bus covers 315 km in 7 hours.
- Speed of the bus = \(\frac{\text{Distance}}{\text{Time}}\) = \(\frac{315 \text{ km}}{7 \text{ hours}}\) = 45 km/h.

### Step 2: Determine the speed of the train.
- It is given that the speed of the bus is three-fourths of the speed of the train.
- Let the speed of the train be \( T \).
- Therefore, \( \frac{3}{4} T = 45 \) km/h.

To find the speed of the train (\( T \)):

\[
T = \frac{45 \times 4}{3} = 60 \text{ km/h}
\]

### Step 3: Determine the speed of the car.
- The ratio of the speed of the train to the car is 12:11.
- If the speed of the train is 60 km/h, then the speed of the car (\( C \)) is given by:

\[
\frac{T}{C} = \frac{12}{11} \implies C = \frac{11}{12} \times 60 = 55 \text{ km/h}
\]

### Step 4: Determine the distance covered by the car in 6 hours.
- Distance covered by the car = Speed of the car \(\times\) Time
- Distance = 55 km/h \(\times\) 6 hours = 330 km

### Conclusion:
The car will cover **330 km** in 6 hours.

The correct option is **330 km**.

Would you like to go over the details or have any further questions?

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Here are 5 related questions to further your understanding:
1. If the train's speed was increased by 20%, how far would it travel in 5 hours?
2. If the car took a different route and traveled for 7 hours, how far would it go?
3. How long would it take for the train to cover a distance of 360 km at its current speed?
4. What is the time difference in hours between the train and car covering 660 km?
5. If the speed ratio was reversed (11:12), how far would the car travel in 4 hours?

**Tip:** Always double-check unit consistency (e.g., km/h for speed and hours for time) when solving speed and distance problems to avoid errors.

Explore a detailed solution to a speed and distance problem involving a train, car, and bus. Understand how to calculate distances based on ratios and speeds. Suitable for Grades 7-9.

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