Discussion
John, Joni and Janardan start running at same time from the same point on a circular track of 70 meters radius. John and Joni run clockwise and Janardan runs
counter clockwise. If John meets Janardan every 66 seconds and Joni meets Janardan every 110 seconds, how frequently(in seconds) will John meet Joni?
Answer: A
The track's length is
\[ C = 2\pi r = 2 \times \frac{22}{7} \times 70 = 440 \text{ m} \]
Runners moving in opposite directions meet once every time their combined distance equals one lap:
\[ v_{\text{John}} + v_{\text{Jan}} = \frac{440}{66} = \frac{20}{3} \text{ m/s} \]
\[ v_{\text{Joni}} + v_{\text{Jan}} = \frac{440}{110} = 4 \text{ m/s} \]
Subtracting eliminates Janardan's speed:
\[ v_{\text{John}} - v_{\text{Joni}} = \frac{20}{3} - 4 = \frac{8}{3} \text{ m/s} \]
John and Joni run the same way, so one laps the other when this difference covers a full circuit:
\[ t = \frac{440}{8/3} = 165 \text{ seconds} \]
Same direction means subtract the speeds; opposite directions means add them. Getting that the wrong way round here would give 66 seconds.
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