The distance between two cities (M and N) is 569 km. A train from City M at 8 am travels towards City N at 53 kmph.Another train starts from City N at 9 am and travels to wards City M at 76 kmph. At what time will the trains meet?

Options

A. 12 : 30 pm
B. 1 : 00 pm
C. 2 : 30 pm
D. 1 : 30 pm

Answer

To solve the problem of when the two trains will meet, we can follow these steps:

### Step 1: Determine the distance traveled by Train A before Train B starts.
Train A leaves City M at 8 AM and travels at a speed of 53 km/h. By 9 AM, when Train B starts from City N, Train A has already been traveling for 1 hour.

**Distance traveled by Train A in 1 hour:**
\[ \text{Distance} = \text{Speed} \times \text{Time} = 53 \text{ km/h} \times 1 \text{ h} = 53 \text{ km} \]

### Step 2: Calculate the remaining distance between the two trains at 9 AM.
The total distance between City M and City N is 569 km. After Train A has traveled 53 km, the remaining distance is:
\[ \text{Remaining Distance} = 569 \text{ km} - 53 \text{ km} = 516 \text{ km} \]

### Step 3: Determine the combined speed of both trains.
Train B travels towards City M at a speed of 76 km/h. Since both trains are moving towards each other, we can add their speeds to find the combined speed:
\[ \text{Combined Speed} = 53 \text{ km/h} + 76 \text{ km/h} = 129 \text{ km/h} \]

### Step 4: Calculate the time taken for the trains to meet after 9 AM.
Using the formula for time, where time is equal to distance divided by speed:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{516 \text{ km}}{129 \text{ km/h}} \approx 4 \text{ hours} \]

### Step 5: Determine the meeting time.
Since Train B starts at 9 AM and it takes approximately 4 hours for the trains to meet, we add 4 hours to 9 AM:
\[ 9 \text{ AM} + 4 \text{ hours} = 1 \text{ PM} \]

### Final Answer:
The trains will meet at **1 PM**.

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