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Math Help - algebra

  1. #1
    Member smmmc's Avatar
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    algebra

    1) Jack cycles home from work, a distance of 10x km. Benny leaves at the same time and
    drives the 40x km to his home.
    A. If Jack and Benny arrive at their homes 30 minutes apart
    i. find x, correct to three decimal places
    ii. find the distance from work of each home, correct to the nearest kilometre.
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  2. #2
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    Quote Originally Posted by smmmc View Post
    1) Jack cycles home from work, a distance of 10x km. Benny leaves at the same time and
    drives the 40x km to his home.
    A. If Jack and Benny arrive at their homes 30 minutes apart
    i. find x, correct to three decimal places
    ii. find the distance from work of each home, correct to the nearest kilometre.
    Are you certain that this is the complete question? In my opinion we need a value of the speed with which the two are going.
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  3. #3
    Member smmmc's Avatar
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    this is it
    1. Jack cycles home from work, a distance of 10x km. Benny leaves at the same time and
    drives the 40x km to his home.
    a. Write an expression in terms of x for the time taken for Jack to reach home if he cycles
    at 8 km/h on average.
    b. Write an expression in terms of x for the time taken for Benny to reach home if he
    drives at an average speed of 70 km/h.
    c. In terms of x, find the difference in times of the two journeys.
    d. If Jack and Benny arrive at their homes 30 minutes apart
    i. find x, correct to three decimal places
    ii. find the distance from work of each home, correct to the nearest kilometre.

    im stuck on d
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  4. #4
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    Quote Originally Posted by smmmc View Post
    this is it
    1. Jack cycles home from work, a distance of 10x km. Benny leaves at the same time and
    drives the 40x km to his home.
    a. Write an expression in terms of x for the time taken for Jack to reach home if he cycles
    at 8 km/h on average.
    b. Write an expression in terms of x for the time taken for Benny to reach home if he
    drives at an average speed of 70 km/h.
    c. In terms of x, find the difference in times of the two journeys.
    d. If Jack and Benny arrive at their homes 30 minutes apart
    i. find x, correct to three decimal places
    ii. find the distance from work of each home, correct to the nearest kilometre.

    im stuck on d
    Use the definition:

    speed = \dfrac{distance}{elapsed \ time}~\implies~elapsed\ time = \dfrac{distance}{speed}

    a) d = 10x km, s = 8 km/h, therefore t_J=\dfrac{10x}8=\dfrac54 x

    b) d = 40x km, s = 70 km/h, therefore t_B=\dfrac{40x}{70}=\dfrac47 x

    c) \Delta(t)=t_J - t_B = \dfrac{19}{28} x

    d) 30 min = 0.5 h that means: \Delta(t)= \dfrac12

    \dfrac{19}{28} x = \dfrac12~\implies~x = \dfrac{14}{19} \approx 0.737

    From the definition given above you get: distance = speed \cdot elapsed\ time

    Jack: d_J=8\frac{km}{h} \cdot \left(\dfrac54 \cdot \dfrac{14}{15}\right)\ h = \dfrac{140}{19}\ km\approx 7\ km

    Ben: d_J=70\frac{km}{h} \cdot \left(\dfrac47 \cdot \dfrac{14}{15}\right)\ h = \dfrac{560}{19}\ km\approx 29\ km
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  5. #5
    Member smmmc's Avatar
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    hey thanks

    but where did you get the 14/15 from?
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  6. #6
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    Quote Originally Posted by smmmc View Post
    hey thanks

    but where did you get the 14/15 from?
    It's one of my silly typos: Actually it is \dfrac{14}{19} - but the result is correct (compare the denominators!)
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