Two buses travel to a place at 45 km/hr, and 60 km/hr. respectively. If the second bus takes `5(1)/(2)` hours less than the first for the journey, the length of the journey is

Options

A. 900km
B. 945km
C. 990km
D. 1350km

Answer

To solve the problem, we need to find the length of the journey based on the speeds of the two buses and the time difference between their journeys.

### Step-by-Step Solution:

1. **Define Variables:**
Let the time taken by the first bus be \( t \) hours. The speed of the first bus is 45 km/hr, and the speed of the second bus is 60 km/hr. According to the problem, the second bus takes \( 5 \frac{1}{2} \) hours (which is \( \frac{11}{2} \) hours) less than the first bus. Therefore, the time taken by the second bus is:
\[ t - \frac{11}{2} \text{ hours} \]

2. **Set Up the Distance Equation:**
The distance traveled by both buses is the same. We can express the distance in terms of speed and time:
- Distance for the first bus: \( \text{Distance} = \text{Speed} \times \text{Time} = 45t \)
- Distance for the second bus: \( \text{Distance} = 60 \left( t - \frac{11}{2} \right) \)

Setting these two distances equal gives us:
\[ 45t = 60 \left( t - \frac{11}{2} \right) \]

3. **Expand and Simplify the Equation:**
Expanding the right side:
\[ 45t = 60t - 60 \times \frac{11}{2} \]
\[ 45t = 60t - 330 \]

4. **Rearrange the Equation:**
To isolate \( t \), we can rearrange the equation:
\[ 45t - 60t = -330 \]
\[ -15t = -330 \]
Dividing both sides by -15:
\[ t = \frac{330}{15} = 22 \text{ hours} \]

5. **Calculate the Distance:**
Now that we have the time taken by the first bus, we can calculate the distance:
\[ \text{Distance} = 45t = 45 \times 22 = 990 \text{ km} \]

### Final Answer:
The length of the journey is **990 km**.