On a 2200 m long circular track, Sarita and Kavita drove their cycles from the same point but in opposite direction with the speeds 20 km/hr and 16 km/hr, respectively. After how much time will they meet again for the first time?
3 minutes 40 seconds
To solve this problem, we need to determine how much time it will take for Sarita and Kavita, traveling in opposite directions on a circular track, to meet again for the first time.
Given:
- Length of the circular track = 2200 meters
- Speed of Sarita = 20 km/hr
- Speed of Kavita = 16 km/hr
First, we convert their speeds from km/hr to m/s, as the track length is given in meters. The conversion factor is \(1 \text{ km/hr} = \frac{5}{18} \text{ m/s}\).
- Speed of Sarita in m/s = \(20 \times \frac{5}{18} = \frac{100}{18} \approx 5.56 \text{ m/s}\)
- Speed of Kavita in m/s = \(16 \times \frac{5}{18} = \frac{80}{18} \approx 4.44 \text{ m/s}\)
Since they are moving in opposite directions, their relative speed is the sum of their speeds:
v_{\text{relative}} = 5.56 + 4.44 = 10 \text{ m/s}
Since the track is circular, they will meet when the sum of the distances they travel equals the length of the track:
Time taken to meet = Total Distance / Relative Speed
t = \frac{2200}{10} = 220 \text{ seconds}
We convert 220 seconds into minutes and seconds:
- 220 seconds = 3 minutes and 40 seconds (since 60 seconds make 1 minute).
Thus, Sarita and Kavita will meet again for the first time after 3 minutes and 40 seconds.
Therefore, the correct answer is:
3 minutes 40 seconds
3 minutes 40 seconds
Relative speed = \( 20 + 16 = 36 \, \text{km/hr} = 10 \, \text{m/s} \)
Distance to meet = 2200 m
Time = \( \frac{2200}{10} = 220 \, \text{seconds} = 3 \, \text{minutes} \, 40 \, \text{seconds} \)
Answer:
3 minutes 40 seconds
3 minutes 40 seconds
Step 1: Convert speeds to m/s
\[ \text{Sarita's speed} = 20\ \text{km/hr} = 20 \times \frac{1000}{3600} = \frac{50}{9}\ \text{m/s} \]
\[ \text{Kavita's speed} = 16\ \text{km/hr} = 16 \times \frac{1000}{3600} = \frac{40}{9}\ \text{m/s} \]
Step 2: Calculate relative speed (opposite directions)
\[ \text{Relative speed} = \frac{50}{9} + \frac{40}{9} = \frac{90}{9} = 10\ \text{m/s} \]
Step 3: Determine meeting time
\[ \text{Time} = \frac{\text{Total distance}}{\text{Relative speed}} = \frac{2200\ \text{m}}{10\ \text{m/s}} = 220\ \text{seconds} \]
Convert to minutes: \[ 220\ \text{seconds} = 3\ \text{minutes}\ 40\ \text{seconds} \]
Final Answer:
They will meet again after \[ \boxed{3\ \text{minutes}\ 40\ \text{seconds}} \].
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