The ratio of speeds, of a Bus and Car is 6:7. If car covers 364 km distance in 4 hours, what is the speed of Bus?

Options

A. 60 km/h
B. 72 km/h
C. 78 km/h
D. 84 km/h

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Determine the speed of the car
The speed of the car can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Given that the car covers a distance of 364 km in 4 hours, we can substitute these values into the formula:
\[ \text{Speed of Car} = \frac{364 \text{ km}}{4 \text{ hours}} = 91 \text{ km/h} \]

### Step 2: Set up the ratio of speeds
We know that the ratio of the speed of the bus to the speed of the car is given as 6:7. Let the speed of the bus be \(6x\) and the speed of the car be \(7x\).

### Step 3: Relate the speed of the car to the ratio
From the previous step, we found the speed of the car to be 91 km/h. Therefore, we can set up the equation:
\[ 7x = 91 \]

### Step 4: Solve for \(x\)
To find \(x\), we divide both sides of the equation by 7:
\[ x = \frac{91}{7} = 13 \]

### Step 5: Calculate the speed of the bus
Now that we have \(x\), we can find the speed of the bus:
\[ \text{Speed of Bus} = 6x = 6 \times 13 = 78 \text{ km/h} \]

### Final Answer
The speed of the bus is **78 km/h**.

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