Discussion
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 ?
Answer: A
Neena's average speed is 6 km/h.
Average speed is total distance divided by total time, and the time spent stopped counts.
\[ \begin{aligned} \text{first part} &= 12 \times \tfrac{10}{60} = 2 \text{ km} \\ \text{rest} &= 4 - 2 = 2 \text{ km} \\ \text{its time} &= \tfrac{2}{8} \text{ h} = 15 \text{ min} \end{aligned} \]
\[ \begin{aligned} \text{total time} &= 10 + 15 + 15 = 40 \text{ min} \\ \text{average} &= \frac{4}{40/60} = 6 \text{ km/h} \end{aligned} \]
10 km/h is the average of 12 and 8, which ignores both the stop and the time spent at each speed. 8 km/h is only the speed of the second part, and 4 km/h would need a total time of one hour.
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