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Help with visualizing this problem

  1. Jan 11, 2006 #1
    Help with visualizing this problem....

    I am having a bit of brain lock-up at the moment...and just can not seem to see my way through this problem.

    A vehicle takes "t" to travel one mile. If the vehicle's speed was 5 mph faster then the "t" to travel the one mile would of been 11 seconds less. What is the original speed of the vehicle.

    I first thought of the formula d=vt but even with looking at the problem with v1 and v2 and/or t1 and t2 with even making a bunch of drawings ...I am just at a loss. I am beginning to think I do not have enough information.

    Can someone give me a gentle nudge in the right direction to get me back on track?

    Thanks
     
  2. jcsd
  3. Jan 11, 2006 #2

    Tide

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    Science Advisor
    Homework Helper

    You have enough information. You can write two equations with two unknowns, v and t. The rest is just algebra.
     
  4. Jan 11, 2006 #3
    You just need to get your variables straight.

    Let's try splitting the two cases up into vehicle 1 and vehicle 2 and define the following variables:

    Vehicle 1:
    distance: d_1
    velocity: v_1
    time: t_1

    Vehicle 2:
    distance: d_2
    velocity: v_2
    time: t_2


    Ok. So far we've used no information. Let's take each phrase and try to extract information. Again, I'm going to treat the two cases as two different vehicles.

    "A [the first] vehicle takes "t" to travel one mile."

    t_1 = t
    d_1 = 1

    "If the [second] vehicle's speed was 5mph faster...

    v_2 = v_1 + 5

    "... then the 't' to travel one mile..."

    d_2 = 1 = d_1

    "...would of been 11 seconds less."

    t_2 = t_1 - 11 = t - 11


    So now, what you thought was to look at the relationship, d=vt. Let's see what we get when we write out this equation for each vehicle (making substitutions based on our above equations).

    Vehicle 1:
    d_1 = v_1 * t_1
    1 = v_1 * t

    Vehicle 2:
    d_2 = v_2 * t_2
    1 = (v_1 + 5) * (t - 11)

    So you have two equations and two unknowns:
    1 = v_1 * t
    1 = (v_1 + 5) * (t - 11)
     
  5. Jan 11, 2006 #4
    Thanks! Woke up this morning realizing that I was over thinking this problem. Casey
     
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