A car goes one kilometre at 30 km per hour and the goes another kilometre at 40 km per hour. The average speed (in km/hour) 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 for the entire journey of 2 km, we can follow these steps:

### Step 1: Calculate the time taken for each part of the journey.

1. **For the first kilometer at 30 km/h:**
- Time = Distance / Speed
- Time = 1 km / 30 km/h = 1/30 hours

2. **For the second kilometer at 40 km/h:**
- Time = Distance / Speed
- Time = 1 km / 40 km/h = 1/40 hours

### Step 2: Find the total time taken for the entire journey.

- Total time = Time for first kilometer + Time for second kilometer
- Total time = (1/30) + (1/40)

To add these fractions, we need a common denominator. The least common multiple of 30 and 40 is 120.

- Convert (1/30) to have a denominator of 120:
- (1/30) = (4/120)

- Convert (1/40) to have a denominator of 120:
- (1/40) = (3/120)

Now we can add:
- Total time = (4/120) + (3/120) = (7/120) hours

### Step 3: Calculate the average speed.

- Average speed = Total distance / Total time
- Total distance = 2 km
- Average speed = 2 km / (7/120) hours

To divide by a fraction, we multiply by its reciprocal:
- Average speed = 2 km * (120/7) = (240/7) km/h

### Step 4: Simplify the average speed.

- Average speed = 240/7 km/h ≈ 34.29 km/h

### Conclusion:

The average speed of the car for the 2 km journey is approximately 34.29 km/h.