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Bus question

  1. May 28, 2013 #1
    1. The problem statement, all variables and given/known data
    A bus travels 650km in 3 hours less than the other bus whose speed is 15 km/h slower than the speed of the first bus.

    A. Assemble the equation.
    B. Solve the equation and state the speeds of the buses.

    2. Relevant equations



    3. The attempt at a solution
    V = d / t
    Velocity of the first bus = Velocity of the second bus - 15; V1 = 650 / t2 - 3
    Time of the first bus = Time of the second bus - 3; V1 - 15 = 650 / t1 + 3

    I don't really know.
     
  2. jcsd
  3. May 28, 2013 #2
    I'm not even sure If I can use physics equations in a mathematics exam
     
  4. May 28, 2013 #3

    Dick

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    Of course you can use v=d/t. I think you are just getting confused with all the variables. Just pick one. Let t be the time of the faster bus. Now write the velocity relation just using the variable t.
     
  5. May 28, 2013 #4

    haruspex

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    Pls use enough parentheses to avoid confusion.
    You'll do better if you write the second equation using the same two unknowns.
     
  6. May 28, 2013 #5

    Ray Vickson

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    Either use a single t, or else use the two of them properly, as in:
    [tex] V_1 = 650/t_1\\
    V_1 - 15 = 650/t_2\\
    t_2 = t_1 + 3
    [/tex]
    You will have three unknowns ##V_1, t_1, t_2## and three equations, so you ought to be able to solve. Your blunder was to put ##t_2-3## in the first equation and ##t_1 + 3## in the second equation, but never specifying what is the relation between ##t_1## and ##t_2##.

    BTW: if you do insist on putting the +3 and -3 in your two equation, you need to write them properly. What you wrote means, literally,
    [tex] V_1 = \frac{650}{t_2} - 3.[/tex] If you mean
    [tex] V_1 = \frac{650}{t_2 - 3}[/tex] then you need to use parentheses, like this:
    V1 = 650/(t2-3). Do you see the difference?
     
  7. May 29, 2013 #6
    While the advice above is reasonable, I think we're skipping steps here.

    There are FOUR equations in FOUR unknowns to start with. The four unknowns are ##t_1, v_1, t_2, v_2## for the time and velocity of the two buses on the 650km journey.

    One of the equations is
    $$t_1v_1 = 650$$
    ... find the other three equations.

    Then we can reduce the system to TWO equations in TWO unknowns by substitution.

    Then we will be able to reduce to a quadratic equation in one unknown.
     
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