A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road . One car has speed of `27 km h^(-1)` while the other has the speed of `18 km h^(-1)` . The bird starts moving from the first car towards the other and is moving with the speed of `36 km h^(-1)` when the two cars were separated by `36 km`. The total distance covered by the bird is

Options

A. `28.8 km`
B. `38.8 km`
C. `48.8 km `
D. `58.8 km`

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Determine the speeds of the cars and the bird
- Speed of the first car (Car A) = 27 km/h
- Speed of the second car (Car B) = 18 km/h
- Speed of the bird = 36 km/h

### Step 2: Calculate the relative speed of the two cars
Since the two cars are moving towards each other, their relative speed is the sum of their speeds:
\[ \text{Relative Speed} = \text{Speed of Car A} + \text{Speed of Car B} = 27 \text{ km/h} + 18 \text{ km/h} = 45 \text{ km/h} \]

### Step 3: Determine the initial distance between the two cars
The initial distance between the two cars is given as:
\[ \text{Distance} = 36 \text{ km} \]

### Step 4: Calculate the time taken for the two cars to meet
Using the formula for time, which is distance divided by speed:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{36 \text{ km}}{45 \text{ km/h}} = 0.8 \text{ hours} \]

### Step 5: Calculate the distance covered by the bird
The bird flies for the entire time until the cars meet. The distance covered by the bird can be calculated using the formula:
\[ \text{Distance covered by the bird} = \text{Speed of the bird} \times \text{Time} \]
Substituting the known values:
\[ \text{Distance covered by the bird} = 36 \text{ km/h} \times 0.8 \text{ hours} = 28.8 \text{ km} \]

### Final Answer
The total distance covered by the bird is **28.8 km**.

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