A truck covers a distance of 256 km at the speed of 32 km/hr . What is the average speed of a car which travels a distance of 160 km more than the truck in the same time ?

Options

A. 46km/`h^(-1)`
B. 52 km/`h^(-1)`
C. 49km/`h^(-1)`
D. 64 km/`h^(-1)`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the time taken by the truck to cover 256 km.
The formula to calculate time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Given:
- Distance covered by the truck = 256 km
- Speed of the truck = 32 km/hr

Substituting the values:
\[ \text{Time} = \frac{256 \text{ km}}{32 \text{ km/hr}} = 8 \text{ hours} \]

### Step 2: Calculate the distance covered by the car.
The car travels a distance that is 160 km more than the truck. Therefore:
\[ \text{Distance covered by the car} = \text{Distance covered by the truck} + 160 \text{ km} \]
Substituting the values:
\[ \text{Distance covered by the car} = 256 \text{ km} + 160 \text{ km} = 416 \text{ km} \]

### Step 3: Calculate the average speed of the car.
We know the time taken by the car is the same as the time taken by the truck, which is 8 hours. The formula for average speed is:
\[ \text{Average Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values for the car:
\[ \text{Average Speed} = \frac{416 \text{ km}}{8 \text{ hours}} = 52 \text{ km/hr} \]

### Final Answer:
The average speed of the car is **52 km/hr**.

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