Chapter 1


  • 2 May 1994


    I can't wait until school is over. Only two more years and I can finally begin a new chapter of my life. Today, dad helped me out with my homework again. This maths exercise was really confusing, but he helped me figure out how to solve it. He's really good with numbers. No wonder he's so successful with his shop. Yesterday, he asked me again if I wanted to take over his shop. I know it'd make him happy, but I have my own plans and dreams. Once I graduate from school, I'm going to become a top manager and create my own business. I can't wait! Time to sleep now. But first I'll review this maths exercise once again, just to make sure I can present the right answers in class tomorrow.



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    Maths task:

    Due to a technical error, two trains were accidently assigned to the same rail track and are now approaching each other. The communication system of both trains is broken and the conductors don't know about the imminent danger they're in.


    By the time a supervisor at one of the offices notices the problem, the trains are only 140 km away from each other. The speed of train A is 160 km/h; the speed of train B is 120 km/h.


    There's a manual switch that could stop both trains from colliding, but the supervisor is 6,300 metres away from it and he needs to get there first. If he runs at an average speed of 14 km/h, will he be in time to save the trains?


    Task: Solve the math exercise.

    • 3 points for the correct answer
    • 7 points for the correct explanation

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  • The two trains run against each other.

    Their total speed is 160 + 120 = 280 km/h

    The distance between them is 140 km. At a total speed of 280 km.

    The crash in half an hour! (140/280).


    Supervisor is 6,300 metres away = 6.3 km away

    At a speed of 14 km/h, hi will travel 6.3 km in less than half an hour!!!


    Yes he will succeed!

  • Oplossing van Glazenier @ NL201 Euromast


    De supervisor heeft 27 minuten nodig om bij de wissel te komen.

    In die tijd legt trein A 63 km af en trein B 54 km. Samen leggen beide treinen in die tijd 117 km af, dat is minder dan de onderlinge afstand van 140 km.

    De supervisor is dus op tijd bij de wissel.

  • Answer:

    Yes, the supervisor will reach the switch in time to stop the trains.


    Explanation:

    The combined speeds of both trains is 280 km/h. Distance is 140 km so the trains will collide in 30 minutes.

    The supervisor can run at 14 km/hour or 7 km in 30 minutes and he is only 6,3 km away from the switch which will take him 27 minutes. He will have 3 minutes left over to read the manual for the switch, to get rid of the rust and free the switch if it is stuck and to pull the switch to the correct position to stop the trains. Plenty of time.

    If it ain't Dutch, it ain't much!

  • Let us first look at the trains: using non-relativistic mechanics we see that from one train's perspective the other train is moving in with a speed of 160+120=280km/h. Hence the distance to the other train (140km) with be covered in exactly 30min. The supervisor needs to run 6.3km at a speed of 14km/h, thus takes 6.3/14=0.45h=27min. Since 27<30, the supervisor can pull the switch before he sees the trains collide.


    We only need to hope the switch is in the right place...


    Addendum: when considering the relativistic case, in the frame of the switch, the switch will be pulled in 27min (same calculation).

    In the frame of each train, the speed of the other train moving in, is slightly smaller than 280km/h (it is (120+160)/(1+120*160/c^2), where c^2 is the speed of light).

    In the frame of a train the distance to be covered will be shortened by a factor γ (which is different for both trains), so for the train the collision happens a factor γ earlier than for the switch. However the clock in each trains is running slower than the clock in the switch, by the same factor γ. So a train sees the switch being pulled earlier by a factor γ than the switch sees it.

    We conclude that both trains see the switch being pulled earlier than they "see" collision happen, in fact relativity will help avoid the collision.


    PS: γ=1/sqrt(1-v^2/c^2), where v is the speed of the train and c the speed of light

  • Train 1 travelling 160 km/hr = 80 km in 30 mins

    Train 2 travelling 120 km/hr = 60 km in 30 mins

    In 30 mins the trains will have travelled 140m between them

    In 30 mins the trains will crash


    Man has to travel 6,300m to reach the switch. 6,300m = 6.3 Km

    He runs at 14 km/hr, so he can travel 7km in 30 mins

    He will reach the switch in time, providing he is a) reasonably fit, b) doesn’t need to stop to open doors, cross roads etc


    And this doesn’t explain why he has to run nearly 4 miles to hit a switch! Does rail safety mean nothing to the designers of this railway? And why does the supervisor not have a phone???? Lets hope that Adam is employed to review the Health and Safety policies of this Railway!

  • the approaching speed for the two trains is 160+120=280km/h; there are 140 km between them so that means they will meet in 30 min.

    the supervisor can run with a speed of 14000m/h so that means he will cover the 6300m distance in 27 minutes

    the trains will be 3min away from each other, 126km closer than they were when the supervisor started running, that means they still have a distance of 14 km between them, and I think space enough to bring both trains to a stop with emergency brakes

  • Problem:

    Due to a technical error, two trains were accidently assigned to the same rail track and are now approaching each other. The communication system of both trains is broken and the conductors don't know about the imminent danger they're in.




    By the time a supervisor at one of the offices notices the problem, the trains are only 140 km away from each other. The speed of train A is 160 km/h; the speed of train B is 120 km/h.




    There's a manual switch that could stop both trains from colliding, but the supervisor is 6,300 metres away from it and he needs to get there first. If he runs at an average speed of 14 km/h, will he be in time to save the trains?


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    Correct answer: - YES, he will be in time to save the 2 trains!


    Correct explanation:


    1 -The speed of train A is 160 km/h = 160.000 m/h = 2 667 metres / minute


    2 -The speed of train B is 120 km/h = 120.000 m/h = 2 000 metres / minute


    3 -They are 140 km away from each other and will be in touch in 30 minutes:


    Train A - 30 min x 2 667 m = 80 000 mt = 80 Km

    Train B - 30 min x 2 000 m = 60 000 mt = 60 Km

    80 Km + 60 Km = 140 Km in 30 minutes



    4 - The supervisor is 6,300 metres away, at an average speed of 14 km/h:

    14 Km/h = 14 000 m/h = 233 metres / minute

    6,300 / 233 = 27 minutes



    The supervisor arrived early less 3 minutes than the pervasively trains contact.




    LYNA

  • Both trains are on the same track, BUT they are heading in the same direction, with Train A going 160KM in the lead and Train B going at 120KM, behind Train A. The are 140KM apart, but train A is going faster, so the distance between the two is only going to get longer, so they will never meet. The supervisor need not worry as they will not collide.

  • Yes, the supervisor will get there first.

    The two trains have a closing speed of 280 km/h. They will cover the gap of 140 km in 30 minutes.

    Running at an average speed of 14 km/h, the supervisor would be able to run a distance of 7 km in the same 30 minutes. He only need to run for 6.3 km so he will have plenty of time to get to the manual switch first.

  • The supervisor will make it in time.


    This is how it goes:


    The supervisor runs at 14 km/h, that is the same as 3,88 meters per second. He will reach the switch after 1620 seconds.


    Train A travels at 160 km/h, which is the same as 44,44 meters per second. So this train will travel 72000 meters in 1620 seconds. This is 72 km.


    Train B travels at 120 km/h which is the same as 33,33 meters per second. So this train will travel 54000 meters in 1620 seconds. This is 54 km.


    The trains will in total have covered 128 km before the supervisor reaches the switch. They will then still be 12 km apart.

  • Yes.


    The trains are approaching each other with a combined speed of 280 km/h, which means they will eat up the 140 km between them in 30 minutes before coliding.


    The supervisor will be running at a speed of 14 km/h, or 7 km/ 30 min, which means he will reach the 6.3 mark before 30 minutes are up and before the trains have colided.

  • The supervisor needs 27 minutes to get to the switch. The trains are approaching each other with 280 km/h relative speed, so the distance 140 km they will cover in 30 minutes. So it seems the colision can be avoided (regardless that it doesn't make sense at all - trains can't take switches at 160 km/h or stop within a second).

  • Yes.


    The trains are 140 km away and they're compound speed is 280 km/h, so it will take them 30 minutes to reach the collision point.


    The supervisor is 6,300 metres away, or 6.3 kilometres, at 14 km/h the supervisor could cover 7 km in 30 minutes, since he only has to cover 6.3 km he'll be quicker than the trains.

    Currently playing on:

    M1.201 Scandinavia

  • Yes.

    The trains would collide in half an hour (A will go 80 km, B will go 60 km; 80+60=140).

    In half an hour, the supervisor will go 7 km, which is more than 6,3 km (= 6300 m), so he's got plenty of time to do that. If he WANTS to :-)

  • Yes, supervisor could stop it, because trains will meet/collidate after half an hour (30 minutes) - train A distance after 30 minutes is 80 km, train B distance after 30 minutes is 60 km (80+60=140).

    Supervisor run after 30 minutes 7 km, which is more than 6.3 km = 6 300 m.


    michalgigo

    COMM4303 Baltic Sea

  • Yes, he will be ontime

    he needs 27 min to arrive to Manual switch


    The train with 120Km/hr in 27 min will be in Km 54

    The train with 160 Km/hr in 27 min will be in Km 72


    54+72= 126 km

    Distance between trains is 140 Km

    They will stop with a distance one to the other of 14 Km


    this is considering that they stop ones the switch is activated, in theory they need a disacceleration that can cause the trains crash