On a $2200 ext{ m}$ long circular track, Sarita and Kavita start from the same point but in opposite directions with speeds of $20 ext{ km/h}$ and $16 ext{ km/h}$ respectively. After how much time will they meet again for the first time?

Question

On a $2200 	ext{ m}$ long circular track, Sarita and Kavita start from the same point but in opposite directions with speeds of $20 	ext{ km/h}$ and $16 	ext{ km/h}$ respectively. After how much time will they meet again for the first time?

Accepted Answer

**Solution:**

1. Convert speeds from km/h to m/s:
   - Sarita's speed = $20 	imes \frac{1000}{3600} = \frac{20000}{3600} = \frac{50}{9} 	ext{ m/s}$
   - Kavita's speed = $16 	imes \frac{1000}{3600} = \frac{16000}{3600} = \frac{40}{9} 	ext{ m/s}$

2. Since they are moving in opposite directions, their relative speed is the sum of their speeds:
   $$	ext{Relative speed} = \frac{50}{9} + \frac{40}{9} = \frac{90}{9} = 10 	ext{ m/s}$$

3. The length of the track is $2200 	ext{ m}$. They will meet again when the sum of distances covered by both equals the track length.

4. Time taken to meet again:
   $$t = \frac{	ext{Distance}}{	ext{Relative speed}} = \frac{2200}{10} = 220 	ext{ seconds}$$

5. Convert $220$ seconds into minutes and seconds:
   - $220 \div 60 = 3$ minutes and remainder $40$ seconds

**Answer:** 3 minutes 40 seconds

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