A man walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How much time will the man require to cover a distance of 24 km if he completes half of his journey walking and half running?

Answer

To solve the problem step by step, we will break down the journey into two parts: the distance walked and the distance run.

### Step 1: Determine the distances for walking and running
The total distance is 24 km. Since the man completes half of his journey walking and half running, we can calculate the distance for each part.

**Distance walked = Total distance / 2 = 24 km / 2 = 12 km**

**Distance run = Total distance / 2 = 24 km / 2 = 12 km**

### Step 2: Calculate the time taken to walk 12 km
The man walks at a speed of 4 km/hr. We can use the formula for time, which is:

**Time = Distance / Speed**

For walking:

**Time taken to walk = Distance walked / Speed walking = 12 km / 4 km/hr = 3 hours**

### Step 3: Calculate the time taken to run 12 km
The man runs at a speed of 8 km/hr. Again, we will use the same formula for time.

For running:

**Time taken to run = Distance run / Speed running = 12 km / 8 km/hr = 1.5 hours**

### Step 4: Calculate the total time taken for the journey
Now we will add the time taken for walking and running to find the total time.

**Total time = Time taken to walk + Time taken to run = 3 hours + 1.5 hours = 4.5 hours**

### Final Answer
The total time required for the man to cover a distance of 24 km, walking half the distance and running the other half, is **4.5 hours**.

---