A bird files with a speed of 10 km/h and a car moves with uniforms speed of 8 km/h .both start from B towrd A (BA=40km) at the same insatnt . The bird having reached A files back immediately to meet the apporaching car. As shown as it reach the car If fiels back to A. The birds repeats this till both the car and the car and the bird reach A simultaneously .The total distancecovered by the bird is 15`psi` km. Find the value of `psi`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the time taken by the car to reach point A.
The distance from B to A is given as 40 km, and the speed of the car is 8 km/h.

Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can calculate the time taken by the car:
\[ \text{Time}_{\text{car}} = \frac{40 \text{ km}}{8 \text{ km/h}} = 5 \text{ hours} \]

### Step 2: Determine the distance covered by the bird in the same time.
The bird flies at a speed of 10 km/h. Since both the bird and the car reach point A simultaneously, the time taken by the bird is also 5 hours.

Using the same formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
we can calculate the distance covered by the bird:
\[ \text{Distance}_{\text{bird}} = 10 \text{ km/h} \times 5 \text{ hours} = 50 \text{ km} \]

### Step 3: Relate the distance covered by the bird to the given expression.
According to the problem, the total distance covered by the bird is given as \( 15\psi \) km. We have calculated that the distance covered by the bird is 50 km.

Setting these equal gives:
\[ 15\psi = 50 \]

### Step 4: Solve for \( \psi \).
To find \( \psi \), we divide both sides of the equation by 15:
\[ \psi = \frac{50}{15} = \frac{10}{3} \]

### Final Answer:
Thus, the value of \( \psi \) is \( \frac{10}{3} \).

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