Circular Track Meeting Time Calculation
This problem involves calculating the time it takes for two runners, moving in opposite directions on a circular track, to meet for the first time. We can solve this using the concept of relative speed.
Key Information
- Track Length = 400 meters
- Speed of Runner A ($v_A$) = 6 m/s
- Speed of Runner B ($v_B$) = 4 m/s
- Direction: Opposite
Relative Speed Concept
When two objects move in opposite directions, their relative speed is the sum of their individual speeds. This is the speed at which the distance between them decreases.
Relative Speed ($v_{rel}$) = $v_A + v_B$
In this case, $v_{rel} = 6 \text{ m/s} + 4 \text{ m/s} = 10 \text{ m/s}$.
Calculating Meeting Time
For the runners to meet for the first time, the total distance covered by both combined must equal the length of the circular track.
Time = Total Distance / Relative Speed
Time = $\frac{\text{Track Length}}{v_{rel}}$
Time = $\frac{400 \text{ meters}}{10 \text{ m/s}}$
Time = 40 seconds
Conclusion
The runners will meet for the first time after 40 seconds.
Important Questions from Speed Time and Distance
The average speed of a train is 180% of the average speed of a car. The car covers a distance of 990 km in 15 hours. The time taken (in hours) by the train to cover the distance of 891 km is:
If Rohit can cover a distance of 1188 km in 22 hours, then what is the speed of Rohit?
A train is moving at 72 km/hrs. The distance covers in 15 minutes by the train is:
If Sonu is driving a car at a speed of 20 m/s, then in how much time Sonu will cover a distance of 936 km?
A person crosses a 1600 m long street in 4 min. What is his speed (in km/h)?
