A person from A starts to walk at 7 am and reaches B at 11 am similarly A person from B starts to walk at 8 am and reaches A at 11:30 am. Find the time at which the meet each other.

Answer

To solve the problem step by step, we will first analyze the information given and then calculate the time at which both persons meet.

### Step 1: Determine the time taken by each person to travel between points A and B.

- Person from A starts walking at **7 AM** and reaches B at **11 AM**.
- Time taken by the person from A = 11 AM - 7 AM = **4 hours**.

- Person from B starts walking at **8 AM** and reaches A at **11:30 AM**.
- Time taken by the person from B = 11:30 AM - 8 AM = **3.5 hours**.

### Step 2: Calculate the speeds of both persons.

Assuming the distance between A and B is **D**:

- Speed of person from A = Distance / Time = D / 4 hours.
- Speed of person from B = Distance / Time = D / 3.5 hours.

### Step 3: Set up the equation for the meeting point.

Let’s denote the speed of the person from A as \( V_A \) and the speed of the person from B as \( V_B \).

- \( V_A = \frac{D}{4} \)
- \( V_B = \frac{D}{3.5} \)

### Step 4: Find the distance covered by each person until they meet.

Let \( t \) be the time in hours after 7 AM when they meet.

- Distance covered by person from A in time \( t \) = \( V_A \cdot t = \frac{D}{4} \cdot t \).
- Distance covered by person from B in time \( t - 1 \) (since B starts at 8 AM, one hour later) = \( V_B \cdot (t - 1) = \frac{D}{3.5} \cdot (t - 1) \).

### Step 5: Set up the equation based on the total distance.

Since both persons together cover the distance \( D \):

\[ \frac{D}{4} \cdot t + \frac{D}{3.5} \cdot (t - 1) = D \]

### Step 6: Simplify the equation.

Dividing the entire equation by \( D \) (assuming \( D \neq 0 \)):

\[ \frac{t}{4} + \frac{(t - 1)}{3.5} = 1 \]

### Step 7: Solve for \( t \).

Multiplying through by 28 (the least common multiple of 4 and 3.5) to eliminate the denominators:

\[ 7t + 8(t - 1) = 28 \]

Expanding and simplifying:

\[ 7t + 8t - 8 = 28 \]
\[ 15t - 8 = 28 \]
\[ 15t = 36 \]
\[ t = \frac{36}{15} = 2.4 \text{ hours} \]

### Step 8: Convert \( t \) into hours and minutes.

- \( 0.4 \) hours = \( 0.4 \times 60 = 24 \) minutes.
- Therefore, \( t = 2 \) hours and \( 24 \) minutes.

### Step 9: Determine the meeting time.

Since they start meeting after 7 AM:

- Meeting time = 7 AM + 2 hours 24 minutes = **9:24 AM**.

### Final Answer:

The two persons will meet each other at **9:24 AM**.

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