A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in

Options

A. 18 minutes
B. 24 minutes
C. 16 minutes
D. 12 minutes

Answer

To solve the problem step by step, we will analyze the speeds of A, B, and C, and then calculate the time taken by A to cover the same distance that C covers in 72 minutes.

### Step-by-Step Solution:

1. **Define the Speeds**:
- Let the speed of C be \( x \).
- Since B runs thrice as fast as C, the speed of B will be \( 3x \).
- A runs twice as fast as B, so the speed of A will be \( 2 \times 3x = 6x \).

2. **Determine the Distance Covered by C**:
- C runs for 72 minutes. To find the distance covered by C, we use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- The distance covered by C in 72 minutes is:
\[ \text{Distance} = x \times 72 \]

3. **Calculate the Time Taken by A to Cover the Same Distance**:
- We need to find out how long it takes for A to cover the same distance \( x \times 72 \) at his speed \( 6x \).
- Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- The time taken by A to cover the distance is:
\[ \text{Time} = \frac{x \times 72}{6x} \]
- Simplifying this gives:
\[ \text{Time} = \frac{72}{6} = 12 \text{ minutes} \]

4. **Conclusion**:
- Therefore, the time taken by A to cover the distance that C covers in 72 minutes is **12 minutes**.