This question asks us to find the average speed for Shanu's entire two-way journey from home to the office and back. Average speed is calculated by dividing the total distance traveled by the total time taken.

Shanu's Journey Details

We are given the following information:

• Distance from home to office: 5 km
• Time taken to travel to the office: 1 hour
• Time taken to travel back home: 1 hour and 30 minutes

Total Distance Covered

To find the average speed, we first need to calculate the total distance Shanu traveled. The journey consists of two parts:

• Distance traveled from home to office = 5 km
• Distance traveled from office to home = 5 km

Therefore, the total distance is:

$$ \text{Total Distance} = \text{Distance (to office)} + \text{Distance (back home)} $$ $$ \text{Total Distance} = 5 \text{ km} + 5 \text{ km} = 10 \text{ km} $$

Total Time Taken

Next, we calculate the total time taken for the entire journey. We need to ensure the time is in consistent units (hours):

• Time taken to travel to the office = 1 hour
• Time taken to travel back home = 1 hour and 30 minutes. Since 30 minutes is half an hour, this is $1 + 0.5 = 1.5$ hours.

The total time is the sum of the time taken for both parts of the journey:

$$ \text{Total Time} = \text{Time (to office)} + \text{Time (back home)} $$ $$ \text{Total Time} = 1 \text{ hour} + 1.5 \text{ hours} = 2.5 \text{ hours} $$

Average Speed Calculation

Now we can calculate the average speed using the formula:

$$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $$

Plugging in the values we calculated:

$$ \text{Average Speed} = \frac{10 \text{ km}}{2.5 \text{ hours}} $$

To perform the division:

$$ \text{Average Speed} = \frac{10}{2.5} = \frac{100}{25} = 4 $$

So, Shanu's average speed during the two-way journey is 4 km/hr.