A bus travelling at 45 km/h takes 3 h more than that of another bus travelling at 60 km/h to cover the same distance. Then find the distance covered by each but in this journey .

Answer

To solve the problem, we need to find the distance covered by each bus. Let's break it down step by step.

### Step 1: Define the variables
Let the distance covered by both buses be \( D \) kilometers.

### Step 2: Calculate the time taken by each bus
- The time taken by the bus traveling at 45 km/h is given by the formula:
\[ T_1 = \frac{D}{45} \]
- The time taken by the bus traveling at 60 km/h is given by the formula:
\[ T_2 = \frac{D}{60} \]

### Step 3: Set up the equation based on the information given
According to the problem, the bus traveling at 45 km/h takes 3 hours more than the bus traveling at 60 km/h. Therefore, we can write the equation:
\[ T_1 = T_2 + 3 \]
Substituting the expressions for \( T_1 \) and \( T_2 \):
\[ \frac{D}{45} = \frac{D}{60} + 3 \]

### Step 4: Solve the equation
To eliminate the fractions, we can find a common denominator, which is 180. Multiplying the entire equation by 180 gives:
\[ 180 \cdot \frac{D}{45} = 180 \cdot \left(\frac{D}{60} + 3\right) \]
This simplifies to:
\[ 4D = 3D + 540 \]
Now, subtract \( 3D \) from both sides:
\[ 4D - 3D = 540 \]
This simplifies to:
\[ D = 540 \]

### Step 5: Conclusion
The distance covered by each bus in this journey is \( 540 \) kilometers.