Gayatri's Distance from Place T

To find out how far Gayatri is from place T, we need to analyze her movements step by step.

Step 1: Walks 1/2 km towards the west from place T
- Gayatri starts at place T and walks towards the west.
- She covers a distance of 1/2 km in the westward direction.

Step 2: Walks 1 1/3 km towards the east from her current position
- After walking 1/2 km in the westward direction, Gayatri changes her direction and starts walking towards the east.
- She covers a distance of 1 1/3 km in the eastward direction from her current position.

Step 3: Calculating the total distance from place T
- Now, we need to calculate the total distance from place T.
- Gayatri initially walks 1/2 km towards the west, so her position is 1/2 km west of place T.
- Then, she walks 1 1/3 km towards the east from her current position.
- To find her final position, we need to subtract the distance she walked towards the east from the distance she walked towards the west.

Calculations:
- Total distance walked towards the west = 1/2 km
- Total distance walked towards the east = 1 1/3 km = 4/3 km
- Final position = 1/2 km - 4/3 km = (3/6) km - (8/6) km = -5/6 km

Final Answer:
- Gayatri is located at a distance of 5/6 km in the west of place T.