1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?

  2. jcsd
  3. Jan 11, 2006 #2


    User Avatar
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook