A car goes one kilometre at 30 km/h and then goes another kilometre to 40 km/h. The average speed (in km/h) of the car for 2 km is

Options

A. `33(3)/(7)`
B. `33(5)/(7)`
C. 35
D. `34(2)/(7)`

Answer

To find the average speed of the car over a distance of 2 kilometers, we can follow these steps:

### Step 1: Calculate the time taken for the first kilometer at 30 km/h
- **Formula**: Time = Distance / Speed
- **Calculation**:
\[ \text{Time}_1 = \frac{1 \text{ km}}{30 \text{ km/h}} = \frac{1}{30} \text{ hours} \]

### Step 2: Calculate the time taken for the second kilometer at 40 km/h
- **Formula**: Time = Distance / Speed
- **Calculation**:
\[ \text{Time}_2 = \frac{1 \text{ km}}{40 \text{ km/h}} = \frac{1}{40} \text{ hours} \]

### Step 3: Calculate the total time taken for the 2 kilometers
- **Calculation**:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 = \frac{1}{30} + \frac{1}{40} \]
- To add these fractions, find a common denominator (which is 120):
\[ \text{Total Time} = \frac{4}{120} + \frac{3}{120} = \frac{7}{120} \text{ hours} \]

### Step 4: Calculate the total distance traveled
- **Calculation**:
\[ \text{Total Distance} = 1 \text{ km} + 1 \text{ km} = 2 \text{ km} \]

### Step 5: Calculate the average speed
- **Formula**: Average Speed = Total Distance / Total Time
- **Calculation**:
\[ \text{Average Speed} = \frac{2 \text{ km}}{\frac{7}{120} \text{ hours}} = 2 \times \frac{120}{7} = \frac{240}{7} \text{ km/h} \]
- This simplifies to approximately \(34.29 \text{ km/h}\) or \(34 \frac{2}{7} \text{ km/h}\).

### Final Answer
The average speed of the car for the 2 kilometers is \( \frac{240}{7} \text{ km/h} \) or approximately \(34.29 \text{ km/h}\).

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