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 ?

Question

Accepted Answer

To determine Neena's average speed for her journey to the market, we need to calculate the total distance she traveled and the total time she spent on the journey.

1. **Total Distance:**
   - The market is 4 km away from Neena's home. Therefore, the total distance she needs to travel is 4 km.

2. **Total Time:**
   - **First Segment:** Neena travels at a speed of 12 km/h for the first 10 minutes. To convert this time into hours, we use the conversion: 10 minutes = 10/60 hours = 1/6 hours.
     - Distance covered in the first segment = Speed × Time = 12 km/h × 1/6 h = 2 km.
   - **Stop Time:** Neena stops to chat with her friend for 15 minutes, which is 15/60 hours = 1/4 hours.
   - **Second Segment:** After the stop, she resumes her journey at a speed of 8 km/h. Since she has already covered 2 km, she has 2 km left to reach the market.
     - Time taken to cover the remaining 2 km = Distance / Speed = 2 km / 8 km/h = 1/4 hours.

- **Total Time Calculation:**
     - Total time = Time for first segment + Stop time + Time for second segment
     - Total time = 1/6 hours + 1/4 hours + 1/4 hours
     - To add these, we convert them to a common denominator:
       - 1/6 = 2/12
       - 1/4 = 3/12
       - 1/4 = 3/12
     - Total time = 2/12 + 3/12 + 3/12 = 8/12 = 2/3 hours

3. **Average Speed:**
   - Average speed is calculated as Total Distance / Total Time.
   - Average speed = 4 km / (2/3 hours) = 4 km × (3/2) = 6 km/h.

Therefore, Neena's average speed for the journey is 6 km/h, which corresponds to Option 1.

**Explanation for Incorrect Options:**

- **Option 2 (8 km/h):** This option is incorrect because it does not account for the time Neena spent chatting with her friend, which affects the total time and thus the average speed calculation.
  
- **Option 3 (10 km/h):** This option is incorrect as it overestimates the average speed by not considering the stop time and the reduced speed in the second segment of the journey.
  
- **Option 4 (4 km/h):** This option is incorrect because it underestimates the average speed. The calculation of average speed based on the total distance and total time clearly shows that the average speed is higher than 4 km/h.

In conclusion, the correct average speed for Neena's journey is 6 km/h, making Option 1 the correct answer.