A car covers first half of total distance at speed of 50 km/h and other half at the rate of 80 km/h. The average speed of car would be

Options

A. 60.5 km/h
B. 61.5 km/h
C. 100 km/h
D. 58.5 km/h

Answer

To find the average speed of the car that covers the first half of the distance at 50 km/h and the second half at 80 km/h, we can follow these steps:

### Step 1: Define the total distance
Let the total distance covered by the car be \( S \). Therefore, the first half of the distance is \( \frac{S}{2} \) and the second half is also \( \frac{S}{2} \).

### Step 2: Calculate the time taken for the first half
Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For the first half:
\[ 50 = \frac{\frac{S}{2}}{T_1} \]
Rearranging gives:
\[ T_1 = \frac{S/2}{50} = \frac{S}{100} \]

### Step 3: Calculate the time taken for the second half
For the second half:
\[ 80 = \frac{\frac{S}{2}}{T_2} \]
Rearranging gives:
\[ T_2 = \frac{S/2}{80} = \frac{S}{160} \]

### Step 4: Calculate the total time taken
The total time \( T \) taken for the journey is the sum of the times for both halves:
\[ T = T_1 + T_2 = \frac{S}{100} + \frac{S}{160} \]
To add these fractions, we need a common denominator. The least common multiple of 100 and 160 is 800. Thus, we convert the fractions:
\[ T = \frac{8S}{800} + \frac{5S}{800} = \frac{13S}{800} \]

### Step 5: Calculate the average speed
The average speed \( V_{avg} \) is given by the total distance divided by the total time:
\[ V_{avg} = \frac{S}{T} = \frac{S}{\frac{13S}{800}} = \frac{800}{13} \]
Calculating this gives:
\[ V_{avg} \approx 61.54 \text{ km/h} \]

### Final Answer
The average speed of the car is approximately **61.5 km/h**.

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