Walking at the rate of 4kmph a man covers certain distance in 2 hrs 45min. Running at a speed of 16.5 kmph the man will cover the same distance in how many minutes ?

Options

A. 50 min
B. 35min
C. 40min
D. 45min

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert the time from hours and minutes to hours only.
The man walks for 2 hours and 45 minutes. We need to convert this time into hours.

- **Calculation**:
\[ 2 \text{ hours} + 45 \text{ minutes} = 2 + \frac{45}{60} = 2 + 0.75 = 2.75 \text{ hours} \]

### Step 2: Calculate the distance covered while walking.
Using the formula for distance, which is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
The speed while walking is 4 km/h.

- **Calculation**:
\[ \text{Distance} = 4 \text{ km/h} \times 2.75 \text{ hours} = 11 \text{ km} \]

### Step 3: Use the distance to find the time taken while running.
Now, we know the distance is 11 km and the running speed is 16.5 km/h. We need to find the time taken to cover this distance while running.

- **Formula**:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

- **Calculation**:
\[ \text{Time} = \frac{11 \text{ km}}{16.5 \text{ km/h}} = \frac{11}{16.5} \text{ hours} \]

### Step 4: Simplify the fraction to find time in hours.
We can simplify \(\frac{11}{16.5}\).

- **Calculation**:
\[ \frac{11}{16.5} = \frac{11 \times 10}{16.5 \times 10} = \frac{110}{165} = \frac{2}{3} \text{ hours} \]

### Step 5: Convert the time from hours to minutes.
To convert hours into minutes, we multiply by 60.

- **Calculation**:
\[ \text{Time in minutes} = \frac{2}{3} \text{ hours} \times 60 \text{ minutes/hour} = 40 \text{ minutes} \]

### Final Answer:
The man will cover the same distance while running in **40 minutes**.

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