A is twice as fast as B and B is thrice as fast as C is. The journey covered by C in `1(1)/(2)` hours will be covered by A in

Options

A. 15 minutes
B. 20 minutes
C. 30 minutes
D. 1 hour

Answer

To solve the problem, we need to determine how long it will take A to cover the same distance that C covers in \(1 \frac{1}{2}\) hours, given the speed relationships between A, B, and C.

### Step-by-Step Solution

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

2. **Calculate the Distance Covered by C**:
- The time taken by C is \(1 \frac{1}{2}\) hours, which can be converted to an improper fraction:
\[ 1 \frac{1}{2} = \frac{3}{2} \text{ hours} \]
- The distance covered by C in this time is given by:
\[ \text{Distance} = \text{Speed} \times \text{Time} = x \times \frac{3}{2} = \frac{3x}{2} \]

3. **Determine the Time Taken by A**:
- Now, we need to find the time taken by A to cover the same distance \(\frac{3x}{2}\).
- The speed of A is \(6x\).
- Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{3x}{2}}{6x} \]
- Simplifying this expression:
\[ \text{Time} = \frac{3x}{2} \div 6x = \frac{3}{2} \times \frac{1}{6} = \frac{3}{12} = \frac{1}{4} \text{ hours} \]

4. **Convert Time into Minutes**:
- To convert \(\frac{1}{4}\) hours into minutes:
\[ \frac{1}{4} \text{ hours} = \frac{1}{4} \times 60 \text{ minutes} = 15 \text{ minutes} \]

### Final Answer
A will cover the journey in **15 minutes**.