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
- 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?
- 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?
- 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?
- 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 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:
- 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:
- 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?
Two trains of lengths 100 m and 150 m are moving in opposite directions at 40 km/h and 60 km/h, respectively. Find the time taken by the trains (in seconds) to cross each other other.
Important Questions from Relative Speed
In a circular race of 2500 m, a man and a woman start from a point towards opposite directions with speeds of 37 km/h and 35 km/h, respectively. After how much time from the start of the race will they meet for the first time?
- X and Yrun a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
A train of length 600 meters passes another train of length 1000 meters moving in the opposite direction in 96 seconds. If the speed of both the trains is the same, then what is the speed of each train?
The distance between Delhi and Patna is $480$ km. A train starts from Delhi and travels towards Patna at a speed of $60$ kmph. Another train starts from Patna towards Delhi at a speed of $80$ kmph, but starts $1$ hour after the first train. In how much time, after the first train started, will they meet each other?
Ram traveling at the speed of 3 km/h reaches 15 minutes late. Had he walked at 4 km/h, he would have reached 15 minutes earlier. How much distance does Ram have to cover?
