A boy swims in a 100 m long pool. He covers 60 m with a velocity of 20 m/s and covers the rest of the distance with a velocity of 10 m/s. Calculate the average velocity of the boy.

Answer

To solve the problem of calculating the average velocity of the boy swimming in a 100 m long pool, we can follow these steps:

### Step 1: Identify the distances and velocities
- The boy swims a total distance of 100 m.
- He covers the first 60 m with a velocity of 20 m/s.
- He covers the remaining 40 m with a velocity of 10 m/s.

### Step 2: Calculate the time taken for the first part of the swim
- For the first 60 m:
\[ \text{Time} (t_1) = \frac{\text{Distance}}{\text{Velocity}} = \frac{60 \, \text{m}}{20 \, \text{m/s}} = 3 \, \text{s} \]

### Step 3: Calculate the time taken for the second part of the swim
- For the remaining 40 m:
\[ \text{Time} (t_2) = \frac{\text{Distance}}{\text{Velocity}} = \frac{40 \, \text{m}}{10 \, \text{m/s}} = 4 \, \text{s} \]

### Step 4: Calculate the total time taken
- The total time taken (T) is the sum of the time for both parts:
\[ T = t_1 + t_2 = 3 \, \text{s} + 4 \, \text{s} = 7 \, \text{s} \]

### Step 5: Calculate the average velocity
- The average velocity (V_avg) is given by the total distance divided by the total time taken:
\[ V_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{100 \, \text{m}}{7 \, \text{s}} \approx 14.29 \, \text{m/s} \]

### Final Answer
The average velocity of the boy is approximately **14.29 m/s**.

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