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Math Help - physics motion

  1. #1
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    physics motion

    . Two runners approaching each other on a straight track have constant speeds of 4.50 m/s and 3.50 m/s, respectively, when they are 100 m apart. How long will it take for the runners to meet, and at what position will they meet if they maintain these speeds?
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  2. #2
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    well you have 2 equations, the one of the guy running 4.5 /s and the one 100m away running 3.5 m/s. So when wil they meet? when the two equatinos intersect! so when does 4.5x = -3.5x + 100?
    as to the second part, you cannot say where they will meet, since you are only given a distance and not a start/end point. I mean you can tell how many meters each one will run before they meet but you cannot say where.
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  3. #3
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    Hello, cruzangyal!

    Two runners approaching each other on a straight track
    have constant speeds of 4.50 m/s and 3.50 m/s, respectively,
    when they are 100 m apart.
    How long will it take for the runners to meet,
    and at what position will they meet if they maintain these speeds?
    Here's a back-door approach to this problem . . .


    They are approaching each other at a combine speed of 4.50 + 3.50 \:=\:8 m/s.

    It is as if one of them is stopped and the other is approaching at 8 m/s.

    To cover 100 m, it will take: . \frac{100}{8} \:=\:\boxed{12.5\text{ seconds.}}


    In 12.5 seconds, the faster runner has covered: . 4.50 \times12.5 \:=\:56.25\text{ meters}
    . . and the slower runner has covered: . 3.50 \times12.5 \:=\:43.75\text{ meters}

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  4. #4
    Eater of Worlds
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    Perhaps you could think of it this way. Since they're running toward each other, the time until they meet would be 100/(4.5+3.5)=25/2=12.5 seconds.

    In that time one travels (12.5)(4.5)=56.25 m

    and the other (12.5)(3.5)=43.75 m

    The position they meet is like this:

    Code:
                      meeting point
                                 |
                                 |
                                \|/
    ****************************************************
    |<------------ 56.25-------->|<------43.75--------->|
    EDIT: It would appear Soroban and I are on the same 'page' .
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