Neena was cycling to the market to buy some grocery items. The market is 4 km away from her home. She travels at a speed of 12 km/h for first 10 minutes. On her way she meets her friend Nikhat and stops to chat with her for 15 minutes. She resumes her journey at a speed of 8 km/h. What is her average speed for the journey ?

The correct option is 6 km/h.

To find the average speed of Neena's journey, we need to divide the total distance covered by the total time taken for the entire journey.

Step 1: Determine the total distance

The total distance from Neena's home to the market is given as:

$\text{Total Distance}=4\text{km}$

Step 2: Calculate the time taken for each part of the journey

Part 1: Initial travel

Neena travels at a speed of 12 km/h for the first 10 minutes.

${\text{Time}}_1=10\text{minutes}=\frac{10}{60}\text{hours}=\frac{1}{6}\text{hours}$

Distance covered during this time:

${\text{Distance}}_1=\text{Speed}\times {\text{Time}}_1=12\text{km/h}\times \frac{1}{6}\text{h}=2\text{km}$

Part 2: Stopping to chat

She stops to chat with her friend for 15 minutes.

${\text{Time}}_2=15\text{minutes}=\frac{15}{60}\text{hours}=\frac{1}{4}\text{hours}$

Part 3: Resuming the journey

The remaining distance to reach the market is:

${\text{Distance}}_3=4\text{km}-2\text{km}=2\text{km}$

She covers this remaining distance at a speed of 8 km/h. The time taken for this part is:

${\text{Time}}_3=\frac{{\text{Distance}}_3}{\text{Speed}}=\frac{2\text{km}}{8\text{km/h}}=\frac{1}{4}\text{hours}=15\text{minutes}$

Step 3: Calculate the total time taken

$\text{Total Time}={\text{Time}}_1+{\text{Time}}_2+{\text{Time}}_3$

$\text{Total Time}=10\text{min}+15\text{min}+15\text{min}=40\text{minutes}$

Converting total time to hours:

$\text{Total Time}=\frac{40}{60}\text{hours}=\frac{2}{3}\text{hours}$

Step 4: Calculate the average speed

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

$\text{Average Speed}=\frac{4\text{km}}{\frac{2}{3}\text{hours}}=4\times \frac{3}{2}=6\text{km/h}$

Therefore, her average speed for the whole journey is 6 km/h.