A man travels 50 km at speed 25 km/hr and next 40 km at 20 km/h and there after travels 90 km at 15 km/h. His average speed is :

Options

A. a)18 kmph
B. b)25 kmph
C. c)20 kmph
D. d)15 kmph

Answer

To find the average speed of the man over the entire journey, we need to follow these steps:

### Step 1: Calculate the total distance traveled
The total distance is the sum of all the distances traveled in each segment of the journey.

- First segment: 50 km
- Second segment: 40 km
- Third segment: 90 km

**Total Distance = 50 km + 40 km + 90 km = 180 km**

### Step 2: Calculate the time taken for each segment
Next, we need to calculate the time taken for each segment using the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

**For the first segment:**
- Distance = 50 km
- Speed = 25 km/h

\[ \text{Time}_1 = \frac{50 \text{ km}}{25 \text{ km/h}} = 2 \text{ hours} \]

**For the second segment:**
- Distance = 40 km
- Speed = 20 km/h

\[ \text{Time}_2 = \frac{40 \text{ km}}{20 \text{ km/h}} = 2 \text{ hours} \]

**For the third segment:**
- Distance = 90 km
- Speed = 15 km/h

\[ \text{Time}_3 = \frac{90 \text{ km}}{15 \text{ km/h}} = 6 \text{ hours} \]

### Step 3: Calculate the total time taken
Now, we sum up the time taken for each segment.

**Total Time = Time_1 + Time_2 + Time_3**

\[ \text{Total Time} = 2 \text{ hours} + 2 \text{ hours} + 6 \text{ hours} = 10 \text{ hours} \]

### Step 4: Calculate the average speed
Finally, we can calculate the average speed using the formula:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

\[ \text{Average Speed} = \frac{180 \text{ km}}{10 \text{ hours}} = 18 \text{ km/h} \]

### Final Answer:
The average speed of the man is **18 km/h**.

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