A man drives his car uniformly at 30 km/h for three hour After it he covered next 90 km distance with uniform speed of 45 km/hr. Find the average speed of car.

Answer

To find the average speed of the car, we need to follow these steps:

### Step 1: Calculate the distance covered in the first part of the journey.
The man drives his car at a speed of 30 km/h for 3 hours.

\[ \text{Distance}_1 = \text{Speed} \times \text{Time} = 30 \, \text{km/h} \times 3 \, \text{h} = 90 \, \text{km} \]

### Step 2: Calculate the time taken for the second part of the journey.
In the second part, he covers a distance of 90 km at a speed of 45 km/h.

\[ \text{Time}_2 = \frac{\text{Distance}}{\text{Speed}} = \frac{90 \, \text{km}}{45 \, \text{km/h}} = 2 \, \text{h} \]

### Step 3: Calculate the total distance covered.
The total distance covered in both parts of the journey is:

\[ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 90 \, \text{km} + 90 \, \text{km} = 180 \, \text{km} \]

### Step 4: Calculate the total time taken.
The total time taken for the journey is:

\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 3 \, \text{h} + 2 \, \text{h} = 5 \, \text{h} \]

### Step 5: Calculate the average speed.
The average speed is given by the formula:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{180 \, \text{km}}{5 \, \text{h}} = 36 \, \text{km/h} \]

### Step 6: (Optional) Convert average speed to meters per second.
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \):

\[ \text{Average Speed in m/s} = 36 \, \text{km/h} \times \frac{5}{18} = 10 \, \text{m/s} \]

### Final Answer:
The average speed of the car is **36 km/h** or **10 m/s**.

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