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Math Help - Solving Problems with Rational Expressions

  1. #1
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    Solving Problems with Rational Expressions

    This is my first time here, i really hope that i am in the right section. I have having alot of problems with problem solving, i am in solving problems with rational expressions

    This is the question that i have:

    Gloria drives a distance of 90 km in 30 min less time than Jayden drives the same distance. What is the speed of each driver if Gloria drives 1.5 times fast than Jayden.

    I need to first write an equation for this and then solve. How can i do this?
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  2. #2
    Super Member bigwave's Avatar
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    Distance = Rate x Time

    in this case the distance is the same for both so set
    R_GT_G = R_JT_J
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  3. #3
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    Quote Originally Posted by nuckers View Post
    This is my first time here, i really hope that i am in the right section. I have having alot of problems with problem solving, i am in solving problems with rational expressions

    This is the question that i have:

    Gloria drives a distance of 90 km in 30 min less time than Jayden drives the same distance. What is the speed of each driver if Gloria drives 1.5 times fast than Jayden.

    I need to first write an equation for this and then solve. How can i do this?
    From d = vt:

    Jayden: 90 = vt .... (1)

    Gloria: 90 = \frac{3}{2} v \left(t - \frac{1}{2}\right) .... (2)

    Your job is to solve equations (1) and (2) simultaneously for v. I suggest solving for t first ....
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  4. #4
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    Quote Originally Posted by nuckers View Post
    This is my first time here, i really hope that i am in the right section. I have having alot of problems with problem solving, i am in solving problems with rational expressions

    This is the question that i have:

    Gloria drives a distance of 90 km in 30 min less time than Jayden drives the same distance. What is the speed of each driver if Gloria drives 1.5 times fast than Jayden.

    I need to first write an equation for this and then solve. How can i do this?
    Let the time it takes Gloria to drive the 90km be t, where t is measured in mins.

    Therefore, the time it takes Jayden is t + 30.


    Let G represent Gloria's speed, and J represent Jayden's speed.

    Therefore G = \frac{90}{t} and J = \frac{90}{t + 30}.


    We also know that Gloria's speed is 1.5 times faster than Jayden's.

    So G = \frac{3}{2}J

    \frac{90}{t} = \frac{3}{2}\left(\frac{90}{t + 30}\right)

    \frac{90}{t} = \frac{135}{t + 30}

    \frac{t}{90} = \frac{t + 30}{135}

    135t = 90(t + 30)

    135t = 90t + 2700

    45t = 2700

    t = 60.


    So it takes Gloria 60 mins, and Jayden 60 + 30 = 90 mins.
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  5. #5
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    thank you for all your help everyone
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  6. #6
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    Note on units.

    Note: The solution in post #3 will give time in hours and speed in km/hr. The solution in post #4 will give time in minutes and speed in km/min.
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