• CKSTEM
  • Learn 
    • CKSTEM Courses
    • Raisining Champions Workshop
    • New Year, New Dreams, New Successes!
    • CKSTEM Family Challenges
    • Holiday Fun Activities
    • How to Outsmart AI?
    • Doses of Motivation
    • Talent V/S Core Values
    • Problem Solving Strategies
  • Compete 
    • Canadian Innovation Contests
    • Australian Mathematics Contest 2025
    • TIMO
    • BBB Olympiad
    • HKIMO
  • Win 
    • Contest Winners
    • CIC 2024 Winners
    • CIC 2023 Winners
    • CIC 2022 Winners
  • Team 
    • About Us
    • Executives
  • …  
    • CKSTEM
    • Learn 
      • CKSTEM Courses
      • Raisining Champions Workshop
      • New Year, New Dreams, New Successes!
      • CKSTEM Family Challenges
      • Holiday Fun Activities
      • How to Outsmart AI?
      • Doses of Motivation
      • Talent V/S Core Values
      • Problem Solving Strategies
    • Compete 
      • Canadian Innovation Contests
      • Australian Mathematics Contest 2025
      • TIMO
      • BBB Olympiad
      • HKIMO
    • Win 
      • Contest Winners
      • CIC 2024 Winners
      • CIC 2023 Winners
      • CIC 2022 Winners
    • Team 
      • About Us
      • Executives
broken image
broken image
broken image
  • CKSTEM
  • Learn 
    • CKSTEM Courses
    • Raisining Champions Workshop
    • New Year, New Dreams, New Successes!
    • CKSTEM Family Challenges
    • Holiday Fun Activities
    • How to Outsmart AI?
    • Doses of Motivation
    • Talent V/S Core Values
    • Problem Solving Strategies
  • Compete 
    • Canadian Innovation Contests
    • Australian Mathematics Contest 2025
    • TIMO
    • BBB Olympiad
    • HKIMO
  • Win 
    • Contest Winners
    • CIC 2024 Winners
    • CIC 2023 Winners
    • CIC 2022 Winners
  • Team 
    • About Us
    • Executives
  • …  
    • CKSTEM
    • Learn 
      • CKSTEM Courses
      • Raisining Champions Workshop
      • New Year, New Dreams, New Successes!
      • CKSTEM Family Challenges
      • Holiday Fun Activities
      • How to Outsmart AI?
      • Doses of Motivation
      • Talent V/S Core Values
      • Problem Solving Strategies
    • Compete 
      • Canadian Innovation Contests
      • Australian Mathematics Contest 2025
      • TIMO
      • BBB Olympiad
      • HKIMO
    • Win 
      • Contest Winners
      • CIC 2024 Winners
      • CIC 2023 Winners
      • CIC 2022 Winners
    • Team 
      • About Us
      • Executives
  •  
  • Canadian Innovation Contests
    • CKSTEM
    • Learn 
      • CKSTEM Courses
      • Raisining Champions Workshop
      • New Year, New Dreams, New Successes!
      • CKSTEM Family Challenges
      • Holiday Fun Activities
      • How to Outsmart AI?
      • Doses of Motivation
      • Talent V/S Core Values
      • Problem Solving Strategies
    • Compete 
      • Canadian Innovation Contests
      • Australian Mathematics Contest 2025
      • TIMO
      • BBB Olympiad
      • HKIMO
    • Win 
      • Contest Winners
      • CIC 2024 Winners
      • CIC 2023 Winners
      • CIC 2022 Winners
    • Team 
      • About Us
      • Executives
    • …  
      • CKSTEM
      • Learn 
        • CKSTEM Courses
        • Raisining Champions Workshop
        • New Year, New Dreams, New Successes!
        • CKSTEM Family Challenges
        • Holiday Fun Activities
        • How to Outsmart AI?
        • Doses of Motivation
        • Talent V/S Core Values
        • Problem Solving Strategies
      • Compete 
        • Canadian Innovation Contests
        • Australian Mathematics Contest 2025
        • TIMO
        • BBB Olympiad
        • HKIMO
      • Win 
        • Contest Winners
        • CIC 2024 Winners
        • CIC 2023 Winners
        • CIC 2022 Winners
      • Team 
        • About Us
        • Executives
    broken image
    broken image
    broken image
    • CKSTEM
    • Learn 
      • CKSTEM Courses
      • Raisining Champions Workshop
      • New Year, New Dreams, New Successes!
      • CKSTEM Family Challenges
      • Holiday Fun Activities
      • How to Outsmart AI?
      • Doses of Motivation
      • Talent V/S Core Values
      • Problem Solving Strategies
    • Compete 
      • Canadian Innovation Contests
      • Australian Mathematics Contest 2025
      • TIMO
      • BBB Olympiad
      • HKIMO
    • Win 
      • Contest Winners
      • CIC 2024 Winners
      • CIC 2023 Winners
      • CIC 2022 Winners
    • Team 
      • About Us
      • Executives
    • …  
      • CKSTEM
      • Learn 
        • CKSTEM Courses
        • Raisining Champions Workshop
        • New Year, New Dreams, New Successes!
        • CKSTEM Family Challenges
        • Holiday Fun Activities
        • How to Outsmart AI?
        • Doses of Motivation
        • Talent V/S Core Values
        • Problem Solving Strategies
      • Compete 
        • Canadian Innovation Contests
        • Australian Mathematics Contest 2025
        • TIMO
        • BBB Olympiad
        • HKIMO
      • Win 
        • Contest Winners
        • CIC 2024 Winners
        • CIC 2023 Winners
        • CIC 2022 Winners
      • Team 
        • About Us
        • Executives
  •  
  • Canadian Innovation Contests
    broken image
    • CKSTEM
    • Learn
      • CKSTEM Courses
      • Raisining Champions Workshop
      • New Year, New Dreams, New Successes!
      • CKSTEM Family Challenges
      • Holiday Fun Activities
      • How to Outsmart AI?
      • Doses of Motivation
      • Talent V/S Core Values
      • Problem Solving Strategies
    • Compete
      • Canadian Innovation Contests
      • Australian Mathematics Contest 2025
      • TIMO
      • BBB Olympiad
      • HKIMO
    • Win
      • Contest Winners
      • CIC 2024 Winners
      • CIC 2023 Winners
      • CIC 2022 Winners
    • Team
      • About Us
      • Executives
    • Canadian Innovation Contests

      Where should CKSTEM build the school?

      Math In Action

      January 15, 2021 · Math-In-Action,Coach's Corner

      On a straight road going through a village there are two log cabins, 50 meters apart. Where on the road should we build a park so that the total distance from the cabins to the park would be as small as possible?

      Competitive Kids STEM - Building A School

      If we were doing this fairly, the park would be halfway between the two cabins, 25 meters from each cabin, adding up to 50 meters. However, in our problem, the park X can be anywhere on the road between cabins A and B because added together, segments AX and XB will always add up to 50 meters. (For example, if we put the park 10 meters from cabin A, then cabin B would be 40 meters away from it, adding up to 50 meters.)

      Competitive Kids STEM - Building A School

      Now solve the same problem with three and four cabins instead of two. Each cabin is 50 meters apart from the next; where, now, should we put the park?

      The case of three cabins: if we do not take into account the middle cabin, then any point between the first and last cabin would satisfy our conditions. Therefore, the best position for the park is next to the middle cabin.

      broken image

      With four cabins (we will call them A, B, C, and D), let us consider the cabins on the sides (A and D) separately from the middle cabins (B and C). For cabins A and D, any point on line segment AD will work. The distances to A and D from the park will always add up to 150 meters.

      Similarly, for cabins B and C, any point on line segment BC will work. The sum of the distances to B and C from the park will always be 50 meters. Thus the minimum total distance (200 meters) is achieved by building the park anywhere between cabins B and C.

      CAN YOU HELP US NOW?

      100 students live in village A, and 50 in village B. The villages are 3 kilometers apart. If Competitive Kids STEM (CKSTEM) is trying to minimize the total distance of the students' walks to school, where should CKSTEM build the school?

      Competitive Kids STEM - Building A School

      Most likely your intuition will not give you a correct answer. You need to bring math in action to help us find a good place to build a school so that total distance walked by the students is minimum. We understand schools are closed during COVID-ERA but we have to plan for the future. Can you help us out by providing your comments below?

      Numbers are less important to us. We believe in proofs. Can you provide a good proof to support your answer to make it easy for us to accept your recommendation?

      • Practice unlimited brain fertilizers and math drills 
      • Math in Action
        • A delicate relationship - percents, fractions, & decimals
        • Substitution Arithmetic
        • Classic Legacy Puzzles
        • Missing Angles
      • Math Problem Solving Courses 
        • Foundation
        • Intermediate
        • Advanced
        • Math Wizard Jr
        • Math Wizard Sr
      Subscribe
      Previous
      Happy New Year and Vision 2021
      Next
      Missing Angles
       Return to site
      • Profile pictureYashnoor It should be 1 km from the school A and 2 from B. This would mean that each group of children will walk the same length. (100*1=100 for group A and 50*2=100 for B)
        January 15, 2021, 11:09pm · Reply
      • Profile pictureYogesh @Yashnoor@yashnoor how do you know that it is the minimum distance? If school is 0.5 km away A then the total distance will be 50+125 = 175 km which is less than what you have calculated. Can we keep make it even smaller? Try to put together a proof.
        January 16, 2021, 02:24am · Reply
      • Profile pictureYashnoor @YogeshHow would it be 125? it would be 100=100 because the 50 group would do 2 km and 100 would do 1.
        January 16, 2021, 05:32pm · Reply
      • Profile pictureYashnoor @YashnoorI might have found it. If it is right next to 100 (school A) it will be the most minimized way possible, so 0 km from A and 3 from 150. Because we want to minimize, it makes sense to put it next to the school with more, as putting it further and further increases the Distance: students value. The...Read more
        January 16, 2021, 05:35pm · Reply
      • Profile pictureYogesh @YashnoorYou are doing well. Can you prove it algebraically using a variable?
        January 18, 2021, 01:58am · Reply
      • Profile pictureAnoushka Guliani i would put it near school a (with 100 students) because as there is twice the amount of kids there as school b (50 students) they wouldn't have to walk as far, but school b (50 students) would have to walk 3 km to reach the park.
        February 17, 2022, 12:54am · Reply
      Profile picture
      Cancel
      ×
      Store Categories
        Cookie Use
        We use cookies to improve browsing experience, security, and data collection. By accepting, you agree to the use of cookies for advertising and analytics. You can change your cookie settings at any time. Learn More
        Accept all
        Settings
        Decline All
        Cookie Settings
        Necessary Cookies
        These cookies enable core functionality such as security, network management, and accessibility. These cookies can’t be switched off.
        Analytics Cookies
        These cookies help us better understand how visitors interact with our website and help us discover errors.
        Preferences Cookies
        These cookies allow the website to remember choices you've made to provide enhanced functionality and personalization.
        Save