Ashish and Prashant as a warm up exercise are jogging on a circular track Prashant is a better athlete and jogs at $18$ km/hr while Ashish jogs at $9$ km/hr. The circumference of the track is $500$ m. They start from the same point and in the same direction. When will they be together again for the first time(calculate the value in seconds) ?

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Solution

Since Prashant is faster than Ashish he will take a lead and as they keep running the gap between them will also keep widening unlike on a straight track they would meet again even if Prashant is faster than Ashish.
Every second Prashant is taking a lead of
$=$ $[18 \times \frac{5}{18} - 9 \times \frac{5}{18}]$ m $= 2.5$ m over Ashish
Hence, he takes $\frac{500}{2.5} = 200 s$ to take a lead of $500$ m over Ashish.
Hence, they would meet for the first time after $200 s$ .

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