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Thread: 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
    $\displaystyle R_GT_G = R_JT_J$
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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: $\displaystyle 90 = vt$ .... (1)

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

    Your job is to solve equations (1) and (2) simultaneously for $\displaystyle v$. I suggest solving for $\displaystyle t$ 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 $\displaystyle t$, where $\displaystyle t$ is measured in mins.

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


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

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


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

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

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

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

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

    $\displaystyle 135t = 90(t + 30)$

    $\displaystyle 135t = 90t + 2700$

    $\displaystyle 45t = 2700$

    $\displaystyle t = 60$.


    So it takes Gloria 60 mins, and Jayden $\displaystyle 60 + 30 = 90$ 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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