This problem involves calculating the change in distance between two individuals, Raju and Karthik, who are moving at different speeds. Since Karthik is chasing Raju, they are running in the same direction, and we can use the concept of relative speed.
Given Information
- Initial distance between Raju and Karthik: 300 m
- Raju's speed ($v_R$): 10 km/h
- Karthik's speed ($v_K$): 12 km/h
- Time duration ($t$): 6 minutes
Convert Speeds to Consistent Units
To perform calculations, convert speeds from km/h to meters per minute (m/min).
- Raju's speed: $v_R = 10 \text{ km/h} = 10 \times \frac{1000 \text{ m}}{60 \text{ min}} = \frac{10000}{60} \text{ m/min} = \frac{500}{3} \text{ m/min}$
- Karthik's speed: $v_K = 12 \text{ km/h} = 12 \times \frac{1000 \text{ m}}{60 \text{ min}} = \frac{12000}{60} \text{ m/min} = 200 \text{ m/min} $
Calculate Relative Speed
Since Karthik is chasing Raju (running in the same direction) and Karthik is faster, the relative speed at which Karthik closes the distance is the difference between their speeds.
Relative speed ($v_{rel}$) = Karthik's speed - Raju's speed
$v_{rel} = v_K - v_R$ $v_{rel} = 200 \text{ m/min} - \frac{500}{3} \text{ m/min}$ $v_{rel} = \frac{600 - 500}{3} \text{ m/min} = \frac{100}{3} \text{ m/min}$Calculate Distance Closed
Calculate the reduction in distance between them after 6 minutes using the relative speed.
Distance closed = Relative speed $\times$ Time
$ \text{Distance closed} = v_{rel} \times t $ $ \text{Distance closed} = \frac{100}{3} \text{ m/min} \times 6 \text{ min} $ $ \text{Distance closed} = 100 \times 2 \text{ m} = 200 \text{ m} $Determine Final Distance
The initial distance is reduced by the distance closed.
Final distance = Initial distance - Distance closed
$ \text{Final distance} = 300 \text{ m} - 200 \text{ m} $ $ \text{Final distance} = 100 \text{ m} $Therefore, the distance between Raju and Karthik after 6 minutes is 100 m.
Similar Questions
- A bus moving at the speed of 45 km/h overtakes a truck 150 m ahead, going in the same direction in 30 sec. The speed of the truck is:
- Two trains are running in the same direction with the speeds of $32\text{ km/h}$ and $26\text{ km/h}$ respectively from X and Y. If X is $42\text{ km}$ away from Y and if they meet at a point Z beyond Y, then the distance from Y to Z will be:
- Sohan and Mohan start from the school with a speed of 3.5 km/hr and 4 km/hr. What time will they take to be 1.5 km apart if they start in the same direction?
- P can run 250 m in 25 s and Q can run the same distance in 30 s. By what distance is P ahead of Q after 4.5 s, if both start the race at the same time?
- A started a journey at 1:00 p.m. at a speed of 40 km/h. B started from the same spot and in the same direction at 1:40 p.m. at a speed of 50 km/h. How many minutes will B take to catch up with A?
- A carriage driving in a fog passed a man who was walking at the speed of 3 km/h in the same direction. He could see the carriage for 4 min and it was visible to him up to a distance of 100 m. What was the speed of the carriage?
- A dog saw a cat at a distance of 280 m. The cat at once ran with the speed of 10 km/h and the dog also ran to catch it with the speed of 24 km/h. How much time will the dog take to catch the cat?
- Two trains of length 200 m and 400 m run on parallel lines. When they run in the same direction, it takes 30 seconds for the train with the higher speed to overtake the other train, and when they travel in the opposite directions, it takes them 6 seconds to cross each other. What are the speeds (in km/h) of the two trains?
- Ravi and Mohan start moving together from a point in opposite directions on bikes. Ravi's speed is 80 km/h and Mohan's speed is 40 km/h. What will be the distance between them after 15 min?
- Two persons A and B are travelling towards each other at the speeds of 10 km/h and 14 km/h. The distance between them is 24 km. Find the time taken by them to meet each other.
Important Questions from Relative Speed
The driver of a car, which is travelling at a speed of 75 km/h, locates a bus 80 m ahead of him, travelling in the same direction. After 15 seconds, he finds that the bus is 40 m behind the car. What is the speed of the bus (in km/h)?
The distance between two station A and B is 800 km. A train X starts from A and moves towards B at 40 km/h and another trains Y starts from B and moves towards A at 60 km/h. how far from A will they cross each other?
A and B are travelling towards each other from the points P and Q respectively. After crossing each other, A and B take \(6\frac{1}{8}\) hours and 8 hours, respectively, to reach their destinations Q and P, respectively. If the speed of B is 16.8 km/h, then the speed (in km/hr) of A is:
A train leaves station A at 8 am and reaches station B at 12 noon. A car leaves station B at 8:30 am and reaches station A at the same time when the train reaches station B. At what time do they meet?
A and B start moving towards each other from places X and Y respectively, at the same time. The speed of A is 20% more than that of B. After meeting on the way, A and B take \(2\frac{1}{2}\) hours and x hours now to reach Y and X respectively. What is the value of x?
