What will be the time taken by Rahul to cover the same distance which is covered by Abhishek in 5 hours if ratio of speed of Abhishek and Rahul is 6:5?

Options

A. 4 hrs
B. 5 hrs
C. 6 hrs
D. 7 hrs

Answer

To solve the problem, we need to find the time taken by Rahul to cover the same distance that Abhishek covers in 5 hours, given that the ratio of their speeds is 6:5.

### Step-by-Step Solution:

1. **Understand the relationship between speed, time, and distance**:
The formula for distance is given by:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Since both Rahul and Abhishek cover the same distance, we can set up the equation based on their speeds and times.

2. **Define the speeds**:
Let the speed of Abhishek be \(6x\) and the speed of Rahul be \(5x\), where \(x\) is a common factor.

3. **Calculate the distance covered by Abhishek**:
Abhishek covers the distance in 5 hours. Using the distance formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 6x \times 5 = 30x \]

4. **Set up the equation for Rahul's time**:
Let \(t\) be the time taken by Rahul to cover the same distance. Using the distance formula for Rahul:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 5x \times t \]
Since both distances are equal, we can set them equal to each other:
\[ 30x = 5x \times t \]

5. **Solve for \(t\)**:
To find \(t\), divide both sides by \(5x\):
\[ t = \frac{30x}{5x} = 6 \text{ hours} \]

### Conclusion:
The time taken by Rahul to cover the same distance is **6 hours**.