Raju 's school is 4 km away from his house . He walks from his house to school and comes back in `2(1)/(2)` hours . Find his average speed.

Answer

To find Raju's average speed, we can follow these steps:

### Step 1: Determine the total distance traveled
Raju walks from his house to school and then back home. The distance from his house to school is 4 km. Therefore, the total distance he travels is:
\[ \text{Total Distance} = \text{Distance to School} + \text{Distance back Home} = 4 \, \text{km} + 4 \, \text{km} = 8 \, \text{km} \]

### Step 2: Convert the time taken into hours
Raju takes \(2 \frac{1}{2}\) hours to complete his journey. We can convert this mixed number into an improper fraction:
\[ 2 \frac{1}{2} = \frac{5}{2} \, \text{hours} \]

### Step 3: Use the formula for average speed
The formula for average speed is given by:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
Substituting the values we have:
\[ \text{Average Speed} = \frac{8 \, \text{km}}{\frac{5}{2} \, \text{hours}} \]

### Step 4: Simplify the calculation
To divide by a fraction, we multiply by its reciprocal:
\[ \text{Average Speed} = 8 \, \text{km} \times \frac{2}{5} = \frac{16}{5} \, \text{km/h} \]

### Step 5: Convert the fraction into a decimal
Now we can convert \(\frac{16}{5}\) into a decimal:
\[ \frac{16}{5} = 3.2 \, \text{km/h} \]

### Final Answer
Thus, Raju's average speed is:
\[ \text{Average Speed} = 3.2 \, \text{km/h} \]

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