Interview Question: Brotherly Competition

Sample Question #110 (mathematical brainteaser)

My younger brother and I go to the same school. It takes me 20 minutes to walk to the school from home and it takes him 30 minutes. One morning, my brother takes off for school 5 minutes before I. After how many minutes of my walking will I catch up to my brother?

(Comment: according to an article in the New York Times a few months ago, a question similar to this one was asked of 8-year-old Terence Tao, a Chinese-Australian math prodigy who’s now a renowned mathematician at UCLA. He was able to figure out the answer in his head in no time! What a genius. Please try this on your own before peeking at my answer in the Comment section.)

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4 Responses to Interview Question: Brotherly Competition

  1. Brett says:

    ANSWER
     
    Before you start solving the problem, first state the assumption that the two brothers will be walking at their usual speeds.
     
    Let D be the distance between school and home, and x be the time, in minutes, at which point "I" catch up to "my brother."  Notice that by the time "I" walked for x minutes, the two brothers have travelled the same distance.
     
    Then it’s easy.
     
         x * D/20 = (5+x) * D/30
     
    Solve for x. (x=10)
     
    Note: I made up the numbers in the question; I’m not sure if the question Terence Tao was actually given when he was 8 years old involved numbers that made it easier to solve. Still, it’s absolutely amazing an eight-year-old could work out the equation very quickly in his head, without writing anything down. (Unless, of course, he’d already seen the question before!)

  2. Zhe says:

    You only need suppose your brother walk 1 unit/min, and you are 1.5 unit/min. 5×1/(1.5-1)=10min. I guess more than half of Chinese children at 8 years old may solve this problem less than 1 minutes. Terence Tao is a genius, but not at this problem.

  3. Brett says:

    Hehe, when I was an eight-year-old boy in China I only wanted to play soccer, eat cotton candy every day, and chase girls older than myself.  🙂  I remember getting 60 (the passing grade) once in a while in my math classes.
     
    -brett
     

  4. Chunsheng says:

    How about calculating it this way? The brother needs extra 10 min to walk the same distance. He started 5 min earlier so he would need another 5 min after I finish. This is symmetric, so I must have caught him in the mid-way.

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