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Thread: math word problems

  1. #1
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    math word problems

    Here is the last rate problem in my General Knowledge test:

    A bicycle racer covers a 75 mile training route to prepare for an upcoming race. If the racer could increase his speed by 5mph. he could complete the course in three fourths of the time. Find his average speed.
    ---------------------------------------------------------------
    0 75
    Average speed of bicycler= x
    x+5mph/3/4h= 75miles
    well the answer is 15 mph
    I still can t set up an equation right please help.

  2. #2
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    Re: math word problems

    Quote Originally Posted by wrightka
    Here is the last rate problem in my General Knowledge test:

    A bicycle racer covers a 75 mile training route to prepare for an upcoming race. If the racer could increase his speed by 5mph. he could complete the course in three fourths of the time. Find his average speed.
    Code:
    ---------------------------------------------------------------
    0                                                                              75
    Average speed of bicycler= x
    x+5mph/3/4h= 75miles
    well the answer is 15 mph
    I still can t set up an equation right please help.
    Let the initial speed be = x miles/hr
    initial time required to cover the distance = 75/x .................................(1)

    Let the improved speed be = (x+5) miles/hr
    Improved time required to cover the distance = 75/(x+5) .................................(2)

    Then

    If the racer could increase his speed by 5mph. he could complete the course in three fourths of the time

    That says:

    (improved time)/(Initial time) = 3/4 .............................(3) [edited]

    Those are your equations - continue......
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
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    Re: math word problems

    I am still lost. I do not understand the conceptualization part. Here goes anyway:

    (initial time) x (improved time) = 3/4

    (x) x (75/x+5) = 3/4
    x/1 x 75/x+5 =3/4
    am i supposed to cross multiply here?
    x+5(x) =75
    x^2 +5x =75
    dont get it

    X(75)/x+5 =3/4
    75x times 1/x+5 =3/4
    75x/x+5 =3/4
    4(75x)= 3(x+5)
    300x= 3x +15
    300x-3x =15
    297x =15
    19.8 =x
    that,s not right either!!!

  4. #4
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    Re: math word problems

    Quote Originally Posted by wrightka
    (initial time) x (improved time) = 3/4
    (x) x (75/x+5) = 3/4
    You were told this:
    initial time required to cover the distance = 75/x .................................(1)

    Improved time required to cover the distance = 75/(x+5) .................................(2)

    (improved time)/(Initial time) = 3/4 .............................(3)
    So:
    [75 / (x + 5)]/(75 / x) = 3/4

    You wrote that as: (x) x (75/x+5) = 3/4 : WHY?!

    You don't seem to be paying attention.
    I'm just an imagination of your figment !

  5. #5
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    Re: math word problems

    I am an exceptional student with Cerebral Palsey. Can you help me with the mechanics ?


    (75/x)(75/(x+5) = 3/4
    3(75/x) (75(x+5) =3/4
    (225x) =(75x +375)
    225x = 75x + 375
    150x=375
    25x =3/4
    100x=3
    x =.003
    That's not right

  6. #6
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    Re: math word problems

    Quote Originally Posted by wrightka
    I am an exceptional student with Cerebral Palsey. Can you help me with the mechanics ?


    (75/x)(75/(x+5) = 3/4
    3(75/x) (75(x+5) =3/4
    (225x) =(75x +375)
    225x = 75x + 375
    150x=375
    25x =3/4
    100x=3
    x =.003
    That's not right
    [tex]\frac{\left[\frac{75}{x+5} \right ]}{\left [ \frac{75}{x}\right ]} \, = \, \frac{3}{4}[/tex]

    [tex]\frac{75}{x+5} \cdot \frac{x}{75} \, = \, \frac{3}{4}[/tex]

    [tex]\frac{x}{x+5} \, = \, \frac{3}{4}[/tex]

    [tex]4\cdot x \, = 3(x \, + \, 5)[/tex]

    Now continue....
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  7. #7
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    Re: math word problems

    okay now I get it. Thanks

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