Walking at the rate of 4km an hour, a man covers a certain distance in 3 hours 45 minutes. If he covers the same distance on cycle, cycling at the rate of 16.5 km/hour, the time taken by him is

Options

A. 55.45 minutes
B. 54.55 minutes
C. 55.44 minutes
D. 45.55 minutes

Answer

To solve the problem, we need to find the distance covered by the man while walking and then calculate the time taken to cover the same distance while cycling.

### Step-by-Step Solution:

1. **Convert Time to Hours**:
The man walks for 3 hours and 45 minutes. We need to convert this time into hours.
\[ 3 \text{ hours} + 45 \text{ minutes} = 3 + \frac{45}{60} = 3 + 0.75 = 3.75 \text{ hours} \]

**Hint**: Remember that 1 hour = 60 minutes. To convert minutes to hours, divide the number of minutes by 60.

2. **Calculate Distance**:
The distance covered can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Here, the speed is 4 km/h and the time is 3.75 hours.
\[ \text{Distance} = 4 \text{ km/h} \times 3.75 \text{ hours} = 15 \text{ km} \]

**Hint**: To find the distance, multiply the speed by the time. Make sure both speed and time are in compatible units (e.g., km/h and hours).

3. **Calculate Time Taken to Cycle the Same Distance**:
Now, we need to find the time taken to cover the same distance of 15 km while cycling at a speed of 16.5 km/h.
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
We have:
\[ \text{Time} = \frac{15 \text{ km}}{16.5 \text{ km/h}} = \frac{15}{16.5} \text{ hours} \]

**Hint**: To find the time taken for a journey, divide the distance by the speed.

4. **Calculate the Exact Time**:
Now, we can simplify \(\frac{15}{16.5}\):
\[ \frac{15}{16.5} = \frac{1500}{1650} = \frac{100}{110} = \frac{10}{11} \text{ hours} \]
To convert this into minutes:
\[ \frac{10}{11} \text{ hours} \times 60 \text{ minutes/hour} = \frac{600}{11} \approx 54.55 \text{ minutes} \]

**Hint**: To convert hours into minutes, multiply by 60.

### Final Answer:
The time taken by the man to cycle the same distance is approximately **54.55 minutes**.