Two stations A and B are 500 km away. If two buses each start from station A and B simultaneously travelling towards the other station with speeds 80 km/h and 90 km/h , respectively, find the distance between the two buses exactly after 2 h.

Answer

To solve the problem step by step, we will calculate the distance each bus travels in 2 hours and then find the distance between the two buses after that time.

### Step 1: Calculate the distance traveled by Bus X
Bus X travels from station A towards station B at a speed of 80 km/h.

**Distance traveled by Bus X in 2 hours:**
\[ \text{Distance} = \text{Speed} \times \text{Time} = 80 \, \text{km/h} \times 2 \, \text{h} = 160 \, \text{km} \]

### Step 2: Calculate the distance traveled by Bus Y
Bus Y travels from station B towards station A at a speed of 90 km/h.

**Distance traveled by Bus Y in 2 hours:**
\[ \text{Distance} = \text{Speed} \times \text{Time} = 90 \, \text{km/h} \times 2 \, \text{h} = 180 \, \text{km} \]

### Step 3: Calculate the total distance covered by both buses
Now, we add the distances traveled by both buses to find the total distance covered together.

**Total distance covered by both buses:**
\[ \text{Total distance} = \text{Distance by Bus X} + \text{Distance by Bus Y} = 160 \, \text{km} + 180 \, \text{km} = 340 \, \text{km} \]

### Step 4: Calculate the distance between the two buses
The initial distance between the two stations A and B is 500 km. To find the distance between the two buses after 2 hours, we subtract the total distance covered from the initial distance.

**Distance between the two buses:**
\[ \text{Distance between buses} = \text{Initial distance} - \text{Total distance covered} = 500 \, \text{km} - 340 \, \text{km} = 160 \, \text{km} \]

### Final Answer:
The distance between the two buses exactly after 2 hours is **160 km**.

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