Ankita travels 14km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travel 4 km by rickshaw and the remaining distance by bus, she takes 9 minute longer. Find the speed of the rickshaw and of the bus.

Explanation

To solve the problem, we will set up equations based on the information given about Ankita's travel. Let's denote the speed of the rickshaw as \( x \) km/h and the speed of the bus as \( y \) km/h.

### Step 1: Set up the equations based on the first scenario
In the first scenario, Ankita travels 2 km by rickshaw and the remaining distance (which is 14 km - 2 km = 12 km) by bus. The total time taken for this journey is half an hour (30 minutes).

The time taken to travel by rickshaw:
\[
T_1 = \frac{2}{x}
...