Puzzle - How long does it take for the dogs to catch each other and where?

Question:  
                There are four dogs each at the corner of a unit square. Each of the dogs starts chasing the dog in the clockwise direction. They all run at the same speed and continuously change their direction accordingly so that they are always heading straight towards the other dog. How long does it take for the dogs to catch each other and where?

Answer & Explanation: 
                Let the dogs be A, B, C and D where A is chasing B, B is chasing C, C is chasing D and D is chasing A.

All the dogs will eventually meet in the center of the square. Since all the dogs move in symmetry, the only logical answer to the location of their meeting is the center of the square.

At any point in time, dog A is perpendicular to dog B and B perpendicular to C and so on. Dog A moves towards dog B but dog B does not move towards or away from dog A since it is moving perpendicular to dog A. Therefore, the distance that dog A needs to cover to reach dog B is the same as the original distance between them, one unit.

The speed of each of the dog towards the dog it is chasing is given by (1 + cos(t)) where t is the angle on each corner of the square.

Speed of dog = 1 + cos(90) = 1 + 0 = 1
Time needed = Distance/Speed = 1 / 1 = 1 unit.


Liked this question? Share with your friends on Facebook, Twitter, Google+ or Digg!

Do you have a better solution? Let us know through the comments section!

0 comments:

Post a Comment

Your Comment Here!.....

Categories

10th 3i InfoTech Academic Books Accenture ACIO ActiveX ADT Agricultural AIEEE Air Force Algebraic Amdocs Android Answers Application Development Aptitude Aptitude Questions Architectures ASP ATOS B.Sc B.Tech.B.E. Bank Exam BCA BE Board Exam Books break-continue Business Plan C C Programming C# C++ Campus campus interview Candidate profile Capgemini Career CDS Certification CET Challenge Circle Cisco class code Cognizant communication Company Company Profile Competitive Exams computer Computer Networks concentric circles constructor Course Credit Suisse CSS CTS Data Structure DBMS DC Deloitte difficult interview questions dimensions Distributed Computing do while dotNet Download ds Dynamic Web Development e-Admit card Educational engineering entertainment Even Odd Events exam schedule exception for loop fresher GATE general Discussion general knowledge Get Placed Government Job Hall Ticket HCL how to answer How to Prepare HR HR Interview HSC hypertext preprocessor IB IBM IBPS IIT Indian Army Information infosys Intelligence Bureau Internship interview Experience interview questions Interview Tips IntroC IntroC# IntroJava IntroPHP IT J2EE J2ME Java JavaScript jobs Language Books Language Tutorial Languages limit number of objectsJava Limit the number of objects being created in JAVA Linux Linux Administrator Linux Developer Logical Questions loops M Tech M.E. M.Tech M.Tech AND B.Tech Management Management Skills Matrices MBA mca ME microsoft mistakes Mixture Mobile Computing mock questions mock test MySql naukri NDA OOP opening Operating System Oracle paper Persistent PHP php programming php string variables PL/SQL Placement placement guide Placement Paper Placement Process preparing for placement presentation probability Problems Professional program Programming Project Engineer project idea Projects Puzzle qualities Question of the day Questions Quiz Question Recruitment Recruitment Pattern Requirement Result Resume Reviews Screen Sizes Scripting Session Skills Software Software Engineering solved papers Source Code Speed time and distance SQL SSC story Stress Interview Study Material study tips submit resume Synonym TCS Tech Mahindra tech news Technical Books Technical Interview Testing thank you letter Thought Time Table TutC++ Unix questions asked in aptitude and inteviews for MCA UPSC verbal Web Designing Web Developer Website Development What to read while loop Wipro Writing Resume

Receive Quality Tutorials Straight in your Inbox by submitting your Email ID below.

Categories

10th 3i InfoTech Academic Books Accenture ACIO ActiveX ADT Agricultural AIEEE Air Force Algebraic Amdocs Android Answers Application Development Aptitude Aptitude Questions Architectures ASP ATOS B.Sc B.Tech.B.E. Bank Exam BCA BE Board Exam Books break-continue Business Plan C C Programming C# C++ Campus campus interview Candidate profile Capgemini Career CDS Certification CET Challenge Circle Cisco class code Cognizant communication Company Company Profile Competitive Exams computer Computer Networks concentric circles constructor Course Credit Suisse CSS CTS Data Structure DBMS DC Deloitte difficult interview questions dimensions Distributed Computing do while dotNet Download ds Dynamic Web Development e-Admit card Educational engineering entertainment Even Odd Events exam schedule exception for loop fresher GATE general Discussion general knowledge Get Placed Government Job Hall Ticket HCL how to answer How to Prepare HR HR Interview HSC hypertext preprocessor IB IBM IBPS IIT Indian Army Information infosys Intelligence Bureau Internship interview Experience interview questions Interview Tips IntroC IntroC# IntroJava IntroPHP IT J2EE J2ME Java JavaScript jobs Language Books Language Tutorial Languages limit number of objectsJava Limit the number of objects being created in JAVA Linux Linux Administrator Linux Developer Logical Questions loops M Tech M.E. M.Tech M.Tech AND B.Tech Management Management Skills Matrices MBA mca ME microsoft mistakes Mixture Mobile Computing mock questions mock test MySql naukri NDA OOP opening Operating System Oracle paper Persistent PHP php programming php string variables PL/SQL Placement placement guide Placement Paper Placement Process preparing for placement presentation probability Problems Professional program Programming Project Engineer project idea Projects Puzzle qualities Question of the day Questions Quiz Question Recruitment Recruitment Pattern Requirement Result Resume Reviews Screen Sizes Scripting Session Skills Software Software Engineering solved papers Source Code Speed time and distance SQL SSC story Stress Interview Study Material study tips submit resume Synonym TCS Tech Mahindra tech news Technical Books Technical Interview Testing thank you letter Thought Time Table TutC++ Unix questions asked in aptitude and inteviews for MCA UPSC verbal Web Designing Web Developer Website Development What to read while loop Wipro Writing Resume