A covers a certain distance at a certain speed in 8 hours. The speed of B is 4 times the speed of A. B will cover that distance in the time.

Options

A. `2 (1)/(2)` hrs
B. 1 hrs
C. 3 hrs
D. 2 hrs

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Understand the relationship between speeds and times
We know from the problem that:
- A covers a certain distance in 8 hours.
- The speed of B is 4 times the speed of A.

### Step 2: Define the speeds
Let the speed of A be denoted as \( S_A \). Therefore, the speed of B can be defined as:
\[ S_B = 4 \times S_A \]

### Step 3: Use the formula for distance
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Since A covers the distance in 8 hours, we can express the distance covered by A as:
\[ \text{Distance} = S_A \times 8 \]

### Step 4: Express the distance covered by B
Since B covers the same distance, we can express it as:
\[ \text{Distance} = S_B \times T_B \]
Where \( T_B \) is the time taken by B to cover the same distance.

### Step 5: Set the distances equal
Since both A and B cover the same distance, we can set the two equations for distance equal to each other:
\[ S_A \times 8 = S_B \times T_B \]

### Step 6: Substitute \( S_B \) in the equation
Now substituting \( S_B \) with \( 4 \times S_A \):
\[ S_A \times 8 = (4 \times S_A) \times T_B \]

### Step 7: Simplify the equation
We can cancel \( S_A \) from both sides (assuming \( S_A \neq 0 \)):
\[ 8 = 4 \times T_B \]

### Step 8: Solve for \( T_B \)
Now, divide both sides by 4:
\[ T_B = \frac{8}{4} = 2 \text{ hours} \]

### Conclusion
B will cover the distance in **2 hours**.

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