To solve the problem of how far from station B the two trains will meet, we can follow these steps:
### Step 1: Determine the time until the first train starts moving.
The first train (Train T1) leaves station A at 2 PM, while the second train (Train T2) leaves station B at 3:30 PM. Therefore, Train T1 has a head start of 1.5 hours (or 1 hour and 30 minutes).
### Step 2: Calculate the distance covered by Train T1 before Train T2 starts.
Train T1 travels at a speed of 59 km/h. The distance covered by Train T1 in 1.5 hours is:
\[
\text{Distance} = \text{Speed} \times \text{Time} = 59 \, \text{km/h} \times 1.5 \, \text{h} = 88.5 \, \text{km}
\]
### Step 3: Determine the remaining distance between the two trains when Train T2 starts.
The total distance between stations A and B is 677 km. After Train T1 has traveled 88.5 km, the remaining distance is:
\[
\text{Remaining Distance} = 677 \, \text{km} - 88.5 \, \text{km} = 588.5 \, \text{km}
\]
### Step 4: Calculate the combined speed of the two trains.
Train T1 continues to travel towards station B at 59 km/h, and Train T2 travels towards station A at 48 km/h. Therefore, their combined speed is:
\[
\text{Combined Speed} = 59 \, \text{km/h} + 48 \, \text{km/h} = 107 \, \text{km/h}
\]
### Step 5: Calculate the time taken for the two trains to meet.
Using the remaining distance and the combined speed, the time taken for the two trains to meet is:
\[
\text{Time} = \frac{\text{Remaining Distance}}{\text{Combined Speed}} = \frac{588.5 \, \text{km}}{107 \, \text{km/h}} \approx 5.49 \, \text{h}
\]
### Step 6: Calculate the distance traveled by Train T2 before they meet.
Now we can find out how far Train T2 travels in this time. The distance traveled by Train T2 is:
\[
\text{Distance} = \text{Speed} \times \text{Time} = 48 \, \text{km/h} \times 5.49 \, \text{h} \approx 263.52 \, \text{km}
\]
### Step 7: Round the distance to the nearest whole number.
Since we need the distance in kilometers, we round 263.52 km to 264 km.
### Conclusion
Therefore, the distance from station B where the two trains meet is approximately **264 km**.
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