Ashok ran around a square plot ABCD once in the following manner. He ran the distance AB and BC at 4 kmph and 6 kmph respectively. He ran the distance CD and DA at 4 kmph and 6 kmph, respectively. His average speed for running from A to C was 4.8 kmph. Find his average speeds for running around the square plot once (in kmph)

Options

A. `3 . 6`
B. 4
C. `4.8`
D. `5.4`

Answer

To solve the problem, we need to find Ashok's average speed for running around the square plot ABCD once. Let's break it down step by step.

### Step 1: Understand the distances and speeds
- The plot is a square, so all sides are equal. Let's denote the length of each side as \( s \).
- Ashok runs:
- From A to B at 4 km/h
- From B to C at 6 km/h
- From C to D at 4 km/h
- From D to A at 6 km/h

### Step 2: Calculate the time taken for each segment
1. **Time from A to B**:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{s}{4} \]

2. **Time from B to C**:
\[ \text{Time} = \frac{s}{6} \]

3. **Time from C to D**:
\[ \text{Time} = \frac{s}{4} \]

4. **Time from D to A**:
\[ \text{Time} = \frac{s}{6} \]

### Step 3: Calculate total time taken to run around the square plot
Now, we will sum up all the times calculated above:
\[ \text{Total Time} = \frac{s}{4} + \frac{s}{6} + \frac{s}{4} + \frac{s}{6} \]

To add these fractions, we need a common denominator. The least common multiple of 4 and 6 is 12.
- Convert each term:
- \(\frac{s}{4} = \frac{3s}{12}\)
- \(\frac{s}{6} = \frac{2s}{12}\)

Now substituting back:
\[ \text{Total Time} = \frac{3s}{12} + \frac{2s}{12} + \frac{3s}{12} + \frac{2s}{12} = \frac{10s}{12} = \frac{5s}{6} \]

### Step 4: Calculate the total distance
The total distance around the square plot is:
\[ \text{Total Distance} = 4s \]

### Step 5: Calculate average speed
Average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
Substituting the values we have:
\[ \text{Average Speed} = \frac{4s}{\frac{5s}{6}} = 4s \times \frac{6}{5s} = \frac{24}{5} = 4.8 \text{ km/h} \]

### Conclusion
The average speed for running around the square plot once is **4.8 km/h**.