A person covers 20 km distance with a speed of 5 km/h, then he covers the next 15 km with a speed of 3 km/h and the last 10 km is covered by him with a speed of 2 km/h. Find out his average speed for the whole journey.

Answer

To find the average speed of the person for the entire journey, we can follow these steps:

### Step 1: Calculate the Total Distance
The total distance covered by the person is the sum of all the distances he traveled:
- First distance = 20 km
- Second distance = 15 km
- Third distance = 10 km

**Total Distance = 20 km + 15 km + 10 km = 45 km**

### Step 2: Calculate the Time Taken for Each Segment
Now, we will calculate the time taken to cover each segment of the journey using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

1. For the first segment (20 km at 5 km/h):
\[ \text{Time}_1 = \frac{20 \text{ km}}{5 \text{ km/h}} = 4 \text{ hours} \]

2. For the second segment (15 km at 3 km/h):
\[ \text{Time}_2 = \frac{15 \text{ km}}{3 \text{ km/h}} = 5 \text{ hours} \]

3. For the third segment (10 km at 2 km/h):
\[ \text{Time}_3 = \frac{10 \text{ km}}{2 \text{ km/h}} = 5 \text{ hours} \]

### Step 3: Calculate the Total Time
Now, we will sum up all the time taken for each segment:
**Total Time = Time_1 + Time_2 + Time_3**
\[ \text{Total Time} = 4 \text{ hours} + 5 \text{ hours} + 5 \text{ hours} = 14 \text{ hours} \]

### Step 4: Calculate the Average Speed
Finally, we can find the average speed using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
\[ \text{Average Speed} = \frac{45 \text{ km}}{14 \text{ hours}} \]

To simplify this:
- 45 divided by 14 gives us 3 with a remainder of 3.
- This can be expressed as a mixed fraction:
\[ 3 \frac{3}{14} \text{ km/h} \]

### Final Answer
The average speed of the person for the whole journey is:
\[ 3 \frac{3}{14} \text{ km/h} \]

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