A woman starts from her home at `9.00` a.m., walks with a speed of `5 km h^(-1)` on straight road up to her office `2.5 km` away, stays at the office up to `5.00 p.m.`, and returns home by an auto with a speed of `25 kmh^(-1)`. Plot the position-time graph of the woman taking home as origin.

Explanation

To solve the problem step by step, we will analyze the woman's journey from her home to her office and back, and then plot the position-time graph based on her movements.

### Step 1: Determine the time taken to walk to the office
- The woman walks from her home to her office, which is 2.5 km away, at a speed of 5 km/h.
- Time taken (t) can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Speed}} = \frac{2.5 \text{ km}}{5 \text{ km/h}} = 0.5 \text{ hours} = 30 \text{ minutes} \]
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