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Math Help - Speed question

  1. #1
    Raj
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    Speed question

    Runner #1 is 35m ahead of Runner #2.
    Runner #1 travels at 1.65m/s and Runner #2 travels at 1.85m/s.
    Both run in the same direction.
    From where they begin, how far does Runner #2 travel before he catches up with Runner #1, how long does it take?

    I know i have to use variables, but i'm lost. Any help please
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by Raj View Post
    Runner #1 is 35m ahead of Runner #2.
    Runner #1 travels at 1.65m/s and Runner #2 travels at 1.85m/s.
    Both run in the same direction.
    From where they begin, how far does Runner #2 travel before he catches up with Runner #1, how long does it take?

    I know i have to use variables, but i'm lost. Any help please
    You want to find what time (and therefore location) where the runners are at the same spot. Runner #1 is 35 meters ahead of the other one, so use a distance equation...

    d=rt

    d_1+D=d_2

    r_1t+D=r_2t

    1.65t+35=1.85t

    35=0.2t

    t=175

    At 175 seconds into the "race", Runner #1 and Runner #2 are in the same spot. Plug t=175 into the original equation: 1.65t+35=1.85t

    323.75=323.75
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  3. #3
    Super Member wingless's Avatar
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    You don't have to use any equation or formula for this question. We will just use our imagination

    (This solution is similar to my post here)

    First, imagine the scene as you're on the ground, standing, looking at the runners. You see that they're 35 m away and running at the same direction at 1.85 m/s and 1.65 m/s.

    Now, imagine the scene as you are Runner #2. You're 35 m behind Runner #1. You both start running. Ignore the grounds. What do you see? You see that Runner #1 gets closer at 0.2 m/s! (it's 1.85 - 1.65). We just calculated the relative speeds. And now, he's 35 m ahead and coming closer at 0.2 m/s. When would you meet? It's so easy,
    V = \frac{x}{t}
    0.15 = \frac{35}{t}
    t = \frac{35}{0.2}
    t = \frac{350}{2} = 175 seconds

    Now you work the rest
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  4. #4
    Raj
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    Quote Originally Posted by wingless View Post
    You don't have to use any equation or formula for this question. We will just use our imagination

    (This solution is similar to my post here)

    First, imagine the scene as you're on the ground, standing, looking at the runners. You see that they're 35 m away and running at the same direction at 1.85 m/s and 1.65 m/s.

    Now, imagine the scene as you are Runner #2. You're 35 m behind Runner #1. You both start running. Ignore the grounds. What do you see? You see that Runner #1 gets closer at 0.2 m/s! (it's 1.85 - 1.65). We just calculated the relative speeds. And now, he's 35 m ahead and coming closer at 0.2 m/s. When would you meet? It's so easy,
    V = \frac{x}{t}
    0.15 = \frac{35}{t}
    t = \frac{35}{0.2}
    t = \frac{350}{2} = 175 seconds

    Now you work the rest
    I really have to remember this way of solving, test in 2 hours so

    Thanks (again)
    Last edited by Raj; February 7th 2008 at 09:34 AM.
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