Catch Up Time Calculation
First, determine the head start distance A has. A starts at 1:00 p.m. and B starts at 1:40 p.m., meaning A travels for 40 minutes before B starts.
Convert the time difference to hours: $40 \text{ min} = \frac{40}{60} \text{ h} = \frac{2}{3} \text{ h}$.
A's speed is $40 \text{ km/h}$. The head start distance is calculated as:
Head Start Distance = $Speed_A \times \text{Time Difference} = 40 \text{ km/h} \times \frac{2}{3} \text{ h} = \frac{80}{3} \text{ km}$.
Next, find the relative speed between A and B. Since they are moving in the same direction, the relative speed is the difference between B's speed and A's speed.
Relative Speed = $Speed_B - Speed_A = 50 \text{ km/h} - 40 \text{ km/h} = 10 \text{ km/h}$.
The time B takes to catch up is the head start distance divided by the relative speed.
Catch Up Time = $\frac{\text{Head Start Distance}}{\text{Relative Speed}} = \frac{\frac{80}{3} \text{ km}}{10 \text{ km/h}} = \frac{80}{3 \times 10} \text{ h} = \frac{8}{3} \text{ h}$.
Finally, convert this time into minutes.
Catch Up Time in Minutes = $\frac{8}{3} \text{ h} \times 60 \text{ min/h} = 8 \times 20 \text{ min} = 160 \text{ minutes}$.
B will take 160 minutes to catch up with A.
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 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?
- Raju is standing away from Karthik at a distance of 300 m. Raju starts running and Karthik chases him. Raju and Karthik run at the rate of 10 km and 12 km per hour respectively. What is the distance between them after 6 minutes?
- 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?
