Abdul, while driving to school, computes the average speed for his trip to be `20 km h^(-1)`. On his return trip along the same route, there is less traffic and the average speed is `30 km h^(-1)`. What is the average speed for Abdul's trip ?

Explanation

To find the average speed for Abdul's round trip, we can follow these steps:

### Step 1: Define the Variables
Let the distance from Abdul's house to school be \( D \).

### Step 2: Calculate the Time Taken for Each Trip
1. **Time taken to go to school (T1)**:
\[ T_1 = \frac{D}{\text{Speed to school}} = \frac{D}{20 \text{ km/h}} \]

2. **Time taken to return home (T2)**:
\[ T_2 = \frac{D}{\text{Speed from school}} = \frac{D}{30 \text{ km/h}} \]

### Step 3: Calculate Total Distance and Total Time
1. **Total Distance for the round trip**:
\[ \text{Total Distance} = D + D = 2D \]

2. **Total Time for the round trip**:
\[ \text{Total Time} = T_1 + T_2 = \frac{D}{20} + \frac{D}{30} \]

### Step 4: Find a Common Denominator for Total Time
To add the times \( T_1 \) and \( T_2 \), we need a common denominator:
- The least common multiple of 20 and 30 is 60.

Convert each time:
\[ T_1 = \frac{D}{20} = \frac{3D}{60} \]
\[ T_2 = \frac{D}{30} = \frac{2D}{60} \]

Now, add them:
\[ \text{Total Time} = \frac{3D}{60} + \frac{2D}{60} = \frac{5D}{60} = \frac{D}{12} \]

### Step 5: Calculate the Average Speed
The average speed for the round trip is given by:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2D}{\frac{D}{12}} \]
Simplifying this:
\[ \text{Average Speed} = 2D \times \frac{12}{D} = 24 \text{ km/h} \]

### Final Answer
Thus, the average speed for Abdul's trip is **24 km/h**.

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