A vehicle travels `4km` with speed of `3km/h` and another `4km` with speed of `5km/h`,then its average speed is

Options

A. `3.75km/h`
B. `4.25km/h`
C. `3.50km/h`
D. `4.00km/h`

Answer

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

### Step 1: Calculate the time taken for the first part of the journey.
The vehicle travels 4 km at a speed of 3 km/h.

Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can calculate the time taken for the first part:
\[ \text{Time}_1 = \frac{4 \text{ km}}{3 \text{ km/h}} = \frac{4}{3} \text{ hours} \approx 1.33 \text{ hours} \]

### Step 2: Calculate the time taken for the second part of the journey.
The vehicle then travels another 4 km at a speed of 5 km/h.

Using the same formula:
\[ \text{Time}_2 = \frac{4 \text{ km}}{5 \text{ km/h}} = \frac{4}{5} \text{ hours} = 0.8 \text{ hours} \]

### Step 3: Calculate the total time taken for the entire journey.
Now, we can find the total time taken by adding the time for both parts:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 = \frac{4}{3} + \frac{4}{5} \]

To add these fractions, we need a common denominator. The least common multiple of 3 and 5 is 15:
\[ \text{Total Time} = \frac{4 \times 5}{3 \times 5} + \frac{4 \times 3}{5 \times 3} = \frac{20}{15} + \frac{12}{15} = \frac{32}{15} \text{ hours} \approx 2.13 \text{ hours} \]

### Step 4: Calculate the total distance traveled.
The total distance traveled is:
\[ \text{Total Distance} = 4 \text{ km} + 4 \text{ km} = 8 \text{ km} \]

### Step 5: Calculate the average speed.
Finally, we can calculate the average speed using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{8 \text{ km}}{\frac{32}{15} \text{ hours}} = 8 \times \frac{15}{32} = \frac{120}{32} \text{ km/h} = 3.75 \text{ km/h} \]

Thus, the average speed of the vehicle is **3.75 km/h**.

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