Certainly! Let's break down the question and solve it step-by-step to find the man's average speed for the entire journey.
### Step 1: Determine the Distance
The distance from point X to point V is given as \( \frac{10}{2} \) km.
Calculating this gives:
[tex]\[ \frac{10}{2} = 5 \text{ km} \][/tex]
So, the distance from X to V is 5 km.
### Step 2: Determine the Total Distance for the Entire Journey
The man walks to V and then returns to X, so he covers this distance twice.
Thus, the total distance covered during the entire journey is:
[tex]\[ 5 \text{ km (to V)} + 5 \text{ km (back to X)} = 10 \text{ km} \][/tex]
### Step 3: Determine the Total Time Taken
We are given the time it took to walk from X to V and to return:
- Time to walk from X to V: 3 hours
- Time to return from V to X: 4 hours
The total time for the entire journey is:
[tex]\[ 3 \text{ hours} + 4 \text{ hours} = 7 \text{ hours} \][/tex]
### Step 4: Calculate the Average Speed
Average speed is calculated as the total distance traveled divided by the total time taken. We have:
[tex]\[ \text{Total Distance} = 10 \text{ km} \][/tex]
[tex]\[ \text{Total Time} = 7 \text{ hours} \][/tex]
So, the average speed is:
[tex]\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{10 \text{ km}}{7 \text{ hours}} \approx 1.429 \text{ km/h} \][/tex]
Therefore, the man's average speed for the entire journey is approximately [tex]\( 1.429 \)[/tex] km/h.
