About Me

In writing the "About Me" portion of this blog I thought about the purpose of the blog - namely, preventing the growth of Socialism & stopping the Death Of Democracy in the American Republic & returning her to the "liberty to abundance" stage of our history. One word descriptions of people's philosophies or purposes are quite often inadequate. I feel that I am "liberal" meaning that I am broad minded, independent, generous, hospitable, & magnanimous. Under these terms "liberal" is a perfectly good word that has been corrupted over the years to mean the person is a left-winger or as Mark Levin more accurately wrote in his book "Liberty & Tyranny" a "statist" - someone looking for government or state control of society. I am certainly not that & have dedicated the blog to fighting this. I believe that I find what I am when I consider whether or not I am a "conservative" & specifically when I ask what is it that I am trying to conserve? It is the libertarian principles that America was founded upon & originally followed. That is the Return To Excellence that this blog is named for & is all about.

Sunday, October 8, 2017

Two-Train Timing Quiz

In deference to the good sports in the readership who enjoy participating in the quizzes I present from time to time, or just like seeing the solutions, the Two-Train Timing quiz below should be enjoyable.
In this case the quiz requires a small amount of math but if you set it up correctly it almost solves itself.
I found the quiz on the National Museum of Mathematics website (www.MoMath.org) after it appeared in the WSJ.
Please let me know how you work the problem.  I will post all correct answers or alternatively will send the solution privately to anyone who requests it if no one figures it out.
Two-Train Timing Quiz
How long does it take a 1.25-mile-long freight train going 30 miles an hour to pass a 0.25-mile-long passenger train going 60 miles an hour in the opposite direction, from the time that the engines first reach each other to the time that the last cars just clear each other?


  1. Sorry could not complete quiz. At school was never good at these type questions

  2. I had a friend help me with the quiz. Still don't get it. Help!!!

  3. Hi Doug!
    Here's my stab at the Train Quiz.
    Hope all is well with you.

    Answer: 1 minute

    Long Train : Length = 1.25 mi, speed = 30 mph
    Short Train: Length = .25 mi, speed = 60 mph

    This is equivalent to:

    Long Train : Length = 1.25 mi, speed = 90 mph

    Short Train: Length = .25 mi, speed = 0 mph (standing still)

    The rear of the Long Train has to travel the length of both trains (1.25 + .25) = 1.5 mi
    1.5 mi / 90 mph = 1 minute

    Another way to look at it:

    At start
    Long Train (30mph): |---.25---|---.25---|---.25---|---.25---|---.25à|
    Short Train (60 mph): |<--.25---|

    After 1 minute
    Long Train travels ½ mile: |---.25---|---.25---|---.25---|---.25---|---.25à|
    Short Train travels 1 mile: |<--.25---|

  4. Doug - My answer is 1 minute.

    1. Since the trains are traveling in opposite direction to each other, the end speed is the combination of the two speeds., i.e. 60 + 30 = 90 m.p.h. = 90/60 = 1.5 m.p.min.

      The length of the trains are 1.25 miles + 0.25 miles = 1.5 miles and that is the length the two trains have to travel for last cars of the two freight trains to clear each other.

      Therefore time taken to travel distance mentioned above is 1.5 m.p.min/1.5 m. = 1 min.

  5. This one is hard..not sure i got it to be honest , but here is how i did it.

    One train is moving 60 MPH which is one mile per minute. The other train is 1 .25 miles long so...if the bigger train was not moving it would take 1.5 minutes to totally pass the larger train (1.25 miles plus the .25 miles of the other train). But the other train is also moving at 30 mph so we have to factor that in. This is where i get lost. I am guessing that at 30 MPH it would take the larger train 30 seconds to pass the other train.(30 mph equals 1/2 mile a minute and .25 miles in 30 seconds) So i would reduce the total time by 30 seconds and I come up with exactly one minute.

  6. Will take a stab at it. If am right will show how.

    .166 minutes to pass each other.

    1. You must be doing something right because 0.166 is correct but not in minutes. 0.166 minutes is less than 10 seconds so the trains would really be flying. Look again @ your units & I think you have it.

    2. OK lets try this for the quiz. For the trains to pass each other will take 1.466 minutes.

      7920 ‘ of train
      MPH of trains is equal to a head on collision at 90 MPH,
      60 min. in 1 hour X 90 = 5400 min.
      7920’ * 5400 min. = 1.466 minutes to pass each other.

      Is the best I can come up with , is different then my first try.

      1.25 + .25 = 1.5 miles of train.
      90 MPH x 60 min. = 5400 min.
      7920’ * 5400 = 1.466 min. to pass

      There is still a gray area in my head just can not clear it.

    3. You have many principles correct but I think you are making it too complicated.

      Do use minutes although 7,920 = 1.5 miles is correct

      Go to your second solution that uses miles

      90 miles/hour X 60 minutes does not equal 5,400 minutes it equals 5,400 miles-minutes/hour – units do not workout to anything useable

      Work 1.5 miles & 90 miles per hour & see how long it takes the trains to pass – & you have it – put the answer in minutes

      Will provide my solution after you make one more try.

    4. I am still getting .0166 min. to pass, will wait for your answer

    5. Imagine two perfectly parallel train tracks with the front of the engines lined up going in the opposite direction @ the speeds specified. The two trains are pulling away from this initial spot @ 90 miles per hour (30 mph + 60 mph). The second spot of concern is when the end of the last cars of each train will be in alignment on the parallel tracks which brings the length of the trains into play (1.25 miles + 0.25 miles = 1.5 miles). So the problem boils down to how long does it take something going 90 miles an hour to go 1.5 miles. 1.5/90 = 0.01667 hours which some people got but forgot to convert to minutes. Multiple 0.01667 hours times 60 minutes per hour & you get 1 minute. You can also recognize that 1.5/90 is 1/60 of an hour or 1 minute.

    6. Darn I was so close, thanks Doug, if I get problems with letters instead of number I am lost at the gate.

  7. Doug,

    Since the length of both trains is 1.5 miles & using the formula D = R * T to find T;

    60 * T + 30 * T = 1.5

    90 * T = 1.5

    T = 1.5/90 = 1/60 = 1 minute to completely pass each other.

  8. The kids came up with 1 mile! Oops, my mistake, they said 1 minute!