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Math Help - distance word problem

  1. #1
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    distance word problem

    i can't find out how to solve this. i know the awnser is 325 km, but i don't know how i came to that.

    a bus traveling ar 65 km/h takes one and a quarter hours less than a truck traveling at 52 km/h from point a to point b. what is the distance bwtween the 2 citys?
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  2. #2
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    Quote Originally Posted by jjulianmooree1 View Post
    i can't find out how to solve this. i know the awnser is 325 km, but i don't know how i came to that.

    a bus traveling ar 65 km/h takes one and a quarter hours less than a truck traveling at 52 km/h from point a to point b. what is the distance bwtween the 2 citys?
    Let the time taken by the truck be t.

    s = v_1t_1 = 65(t-1.25) = 65t - 81.25

    s = v_2t_2 = 52t

    Rearrange 2nd equation

    t = \frac{s}{52}

    sub in that equation into the first equation to find s
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  3. #3
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    ya...but

    i'm in gr. 9. i can't rally understand ters such as subing in and what not. so, basicially i'm saying run that by me again?
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jjulianmooree1 View Post
    i can't find out how to solve this. i know the awnser is 325 km, but i don't know how i came to that.

    a bus traveling ar 65 km/h takes one and a quarter hours less than a truck traveling at 52 km/h from point a to point b. what is the distance bwtween the 2 citys?
    Let x be the distance between the two cities, then

    x=52t

    x=65(t-\frac{5}{4})
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  5. #5
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    oh, that makes more sense. thank you.
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  6. #6
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    once i do this, it becomes x= 65t - 81.25. don't i need to know t in order to solve this?
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  7. #7
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jjulianmooree1 View Post
    once i do this, it becomes x= 65t - 81.25. don't i need to know t in order to solve this?
    Since x equals x (the distance is the same), set the two equations equal:

    52t=65(t-\frac{5}{4})
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  8. #8
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by jjulianmooree1 View Post
    once i do this, it becomes x= 65t - 81.25. don't i need to know t in order to solve this?
    That's where the second equation comes in. The x = \frac{52}{t} one. In my earlier post I rearranged the second equation to make t the subject to facilitate solving the simultaneous equations
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  9. #9
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    oooooooh... that makes a smige more sense.
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  10. #10
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    so...t=-6.25, 325 devided by 6.25= 52...yeah... i kind of see it. isn't there an easyer method to find this? a table perhaps?
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  11. #11
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jjulianmooree1 View Post
    so...t=-6.25, 325 devided by 6.25= 52...yeah... i kind of see it. isn't there an easyer method to find this? a table perhaps?
    What could be easier than solving for t in the above equation?!

    When you find out, tell the world!!!!

    Kidding. Anyway, these problems require practice. That's all.
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