Answer Time & Distance: Thief and Policeman Catch Up

[aprao]

Hai Expert
COuld you please explain to me how to solve the following problems?

Question:
A Thief sees a policeman 100 Metre ahead of him. He Immediately turns back and starts running at 6Kmph. The Policeman chases him at a speed of 8Kmph. After What time does the policeman catch up with the thief ?


Regards
aprao

 

[arildno]

Version 1:
1) Let your origin coincide with your police-man's initial position
How can we write the police-man's subsequent position (measured relative, that is, to the origin) as a function of time?
2) Measured from the policeman's initial position, the thief's initial position is 100.
How can we write the thief's subsequent position (measured relative, that is, to the origin) as a function of time?

3) Since at the time when the policeman catches up with the thief, their positions is the same, you may find an equation for the time by equating their position functions at that time.

Version 2:
Compute the relative velocity the policeman has to the thief.
How long would it take a person runnning with this relative velocity to travel 100 meters?

I strongly suggest you work out the time by both versions, and verify that both versions predict the same time.
This will help you enhancing your understanding of the maths&physics involved.

 

[tacman]

Sure, I would be happy to explain how to solve this problem.

To solve this problem, we need to first understand the relationship between time, distance, and speed. The basic formula for this is: Distance = Speed x Time.

In this problem, we know that the thief starts running at 6Kmph and the policeman is 100 meters ahead of him. This means that the thief has already covered 100 meters when he starts running.

Now, we need to find out how much distance the thief covers before the policeman catches up with him. We can use the formula Distance = Speed x Time for both the thief and the policeman.

For the thief, we have Distance = 6Kmph x Time. We also know that the thief has already covered 100 meters, so we can write this equation as 100 + 6Kmph x Time.

For the policeman, we have Distance = 8Kmph x Time.

Since we know that the thief and the policeman will eventually meet at the same point, we can set these two equations equal to each other and solve for Time.

100 + 6Kmph x Time = 8Kmph x Time

100 = 2Kmph x Time

Time = 100 / 2Kmph

Time = 50 / Kmph

Therefore, it will take the policeman 50 / Kmph hours to catch up with the thief.

I hope this explanation helps you understand how to solve this problem. Let me know if you have any further questions.