A car covers a distance of 450 km at a certain uniform speed (in km/h). The number of hours it takes for the journey is `1/8` of the number representing the speed. The time taken in hours) by the car to cover the distance is:

Options

A. 9
B. 6
C. 6`1/4`
D. 7`1/2`

Answer

To solve the problem step-by-step, we will use the relationship between distance, speed, and time. The formula we will use is:

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

### Step 1: Define the variables
Let the speed of the car be \( x \) km/h. According to the problem, the time taken for the journey is \( \frac{1}{8} \) of the speed. Therefore, we can express the time as:

\[ \text{Time} = \frac{x}{8} \text{ hours} \]

### Step 2: Set up the equation
We know the distance covered by the car is 450 km. Using the formula for distance, we can set up the equation:

\[ 450 = x \times \frac{x}{8} \]

### Step 3: Simplify the equation
Rearranging the equation gives us:

\[ 450 = \frac{x^2}{8} \]

To eliminate the fraction, multiply both sides by 8:

\[ 8 \times 450 = x^2 \]

Calculating the left side:

\[ 3600 = x^2 \]

### Step 4: Solve for \( x \)
Now, take the square root of both sides to find \( x \):

\[ x = \sqrt{3600} \]

Calculating the square root:

\[ x = 60 \text{ km/h} \]

### Step 5: Find the time taken
Now that we have the speed, we can find the time taken using the expression we defined earlier:

\[ \text{Time} = \frac{x}{8} = \frac{60}{8} = 7.5 \text{ hours} \]

### Conclusion
The time taken by the car to cover the distance of 450 km is **7.5 hours**.

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