A man travels 200 km distance with the speed of 40 m/s and next 50 km with the speed of 10 m/s . Find the average speed of man.

Answer

To find the average speed of the man who travels different distances at different speeds, we can follow these steps:

### Step 1: Calculate Total Distance
The total distance traveled by the man is the sum of the two distances:
- First distance = 200 km
- Second distance = 50 km

Total distance = 200 km + 50 km = 250 km

### Step 2: Convert Distance to Meters
Since the speeds are given in meters per second, we need to convert the total distance from kilometers to meters:
- 1 km = 1000 meters
- Total distance in meters = 250 km × 1000 m/km = 250,000 m

### Step 3: Calculate Time for Each Segment
Now, we need to calculate the time taken for each segment of the journey.

#### For the first segment (200 km at 40 m/s):
- Distance = 200 km = 200,000 m
- Speed = 40 m/s
- Time = Distance / Speed = 200,000 m / 40 m/s = 5000 seconds

#### For the second segment (50 km at 10 m/s):
- Distance = 50 km = 50,000 m
- Speed = 10 m/s
- Time = Distance / Speed = 50,000 m / 10 m/s = 5000 seconds

### Step 4: Calculate Total Time
Now, we can find the total time taken for the entire journey:
Total time = Time for first segment + Time for second segment
Total time = 5000 seconds + 5000 seconds = 10000 seconds

### Step 5: Calculate Average Speed
Finally, we can calculate the average speed using the formula:
Average speed = Total distance / Total time
Average speed = 250,000 m / 10,000 s = 25 m/s

### Final Answer
The average speed of the man is **25 m/s**.

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