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Problem Of The Week 47

with 6 comments


The speed of the engine of a train is 150 km/hr. By connecting coaches to the engine its speed decreases. The decrease in speed is given by the function d=x^2+3x-2 (km/hr), where x is the number of coaches connected. Find the minimum speed ( in km/hr) with which the train can run?

1) 1

2 11

3) 22

4) 33

5) None of these

Written by Implex

October 8, 2008 at 12:02 pm

6 Responses

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  1. option 3
    22
    max number of coaches =10
    did by trial and error.

    is there a better way of doing this , instead of just trial and error??

    qwerty

    October 8, 2008 at 12:35 pm

  2. yupp there is

    outtimed

    October 8, 2008 at 12:38 pm

  3. can u please share that method .

    qwerty

    October 8, 2008 at 12:52 pm

  4. let others try at least, after that if no one gets it, i will post the solution

    outtimed

    October 8, 2008 at 1:24 pm

  5. for the egine to push the train the speed should be greater than 0…

    Final speed of train= Speed of engine- decrease in speed.

    At number of couches= 11 the decreease in speed = 121+33-2=152KMPH
    this is not possible, decrease cannot be greater than 150…
    so the number of Coachs has to be 10..with 10 d= 128KMPH

    speed of train, with which it can run= 150-128=22…

    Is this approach fine???

    Ankaj

    October 8, 2008 at 3:37 pm

  6. x^2+3x-2<150 is the limiting case

    solving we get
    x^2+3x-152=0
    x=(-3+-sqrt(617)/2
    so x comes approx 11
    so x should be less than 11
    so x=10

    put x=10 we get 128
    so speed ia 150-128-122

    outtimed

    October 9, 2008 at 6:09 am


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