Two people A and B are at a distance of 260km from each other at 9:00 a.m. A immediately starts moving towards B at a speed of 25km/h and at 11:00 a.m. B starts moving towards A at a speed of 10km/hr. At what time (in p.m) will they meet each other?

Options

A. `5:00`
B. `6:00`
C. `6:30`
D. `7:00`

Answer

To solve the problem step by step, we will follow the details provided in the question.

### Step 1: Determine the initial distance and the time A travels alone
- The initial distance between A and B is 260 km.
- A starts moving towards B at 9:00 a.m. at a speed of 25 km/h.
- B starts moving towards A at 11:00 a.m. at a speed of 10 km/h.
- From 9:00 a.m. to 11:00 a.m., A travels alone for 2 hours.

**Calculation:**
- Distance traveled by A in 2 hours = Speed × Time = 25 km/h × 2 hours = 50 km.

### Step 2: Calculate the remaining distance after A's travel
- Remaining distance after A has traveled = Initial distance - Distance traveled by A
- Remaining distance = 260 km - 50 km = 210 km.

### Step 3: Determine the relative speed of A and B
- After 11:00 a.m., both A and B are moving towards each other.
- Speed of A = 25 km/h
- Speed of B = 10 km/h
- Relative speed = Speed of A + Speed of B = 25 km/h + 10 km/h = 35 km/h.

### Step 4: Calculate the time taken to meet after 11:00 a.m.
- We need to find the time taken to cover the remaining distance of 210 km at a relative speed of 35 km/h.

**Calculation:**
- Time = Distance / Speed = 210 km / 35 km/h = 6 hours.

### Step 5: Determine the meeting time
- Since B starts moving at 11:00 a.m. and they take 6 hours to meet:
- Meeting time = 11:00 a.m. + 6 hours = 5:00 p.m.

### Final Answer:
- A and B will meet at **5:00 p.m.**.

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