Answer Key 8.8

  1. Who or What Rate Time Equation
    A 20 t 20t
    B 25 t 25t

    20t+25t=60

  2. Who or What Rate Time Equation
    A1 r 6 6r
    A1 r+s 6 6(r+s)

    6r+6(r+s)=276

  3. Who or What Rate Time Equation
    T1 25 t 25t
    T2 40 t 40t

    25t+40t=195

  4. Who or What Rate Time Equation
    J 20 5 20(5)
    S r 5 r(5)

    20(5)+5r=150

  5. Who or What Rate Time Equation
    P r+15 4 4(r+15)
    F r 4 4r

    4(r+15)+4r=300

  6. Who or What Rate Time Equation
    A1 25 t 25t
    A2 35 t 35t

    25t+35t=180

  7. Who or What Rate Time Equation
    Away 10 t 10(t)
    Return 3 10-t 3(10-t)

    10t=3(10-t)

  8. Who or What Rate Time Equation
    w 4 t 4t
    r 20 (3-t) 20(3-t)

    4t=20(3-t)

  9. Who or What Rate Time Equation
    Away 28 t 28t
    Back 4 2-t 4(2-t)

    \begin{array}{rrlrr} 28t&=&4(2&-&t) \\ 28t&=&8&-&4t \\ +4t&&&+&4t \\ \midrule \dfrac{32t}{32}&=&\dfrac{8}{32}&& \\ \\ t&=&\dfrac{1}{4}&& \\ \\ d&=&rt&& \\ d&=&28(\dfrac{1}{4})&& \\ d&=&7\text{ km}&&  \end{array}

  10. Who or What Rate Time Equation
    Leave 15 t 15t
    Return 10 5-t 10(5-t)

    \begin{array}{rrlrr} 15t&=&10(5&-&t) \\ 15t&=&50&-&10t \\ +10t&&&+&10t \\ \midrule \dfrac{25t}{25}&=&\dfrac{50}{25}&& \\ \\ t&=&2&& \\ \\ d&=&rt&& \\ d&=&15(2)&& \\ d&=&30\text{ km}&& \end{array}

  11. Who or What Rate Time Equation
    To resort 30 t 30t
    Return 50 8-t 50(8-t)

    \begin{array}{rrlrr} 30t&=&50(8&-&t) \\ 30t&=&400&-&50t \\ +50t&&&+&50t \\ \midrule \dfrac{80t}{80}&=&\dfrac{400}{80}&& \\ \\ t&=&5&& \\ \\ d&=&rt&& \\ d&=&30(5)&& \\ d&=&150\text{ km}&& \end{array}

  12. Who or What Rate Time Equation
    To airport 90 t 90t
    Return 120 7-t 120(7-t)

    \begin{array}{rrlrr} 90t&=&120(7&-&t) \\ 90t&=&840&-&120t \\ +120t&&&+&120t \\ \midrule \dfrac{210t}{210}&=&\dfrac{840}{210}&& \\ \\ t&=&4&& \\ \\ d&=&rt&& \\ d&=&90(4)&& \\ d&=&360\text{ km}&& \end{array}

  13. Who or What Rate Time Equation
    Sam 4 t 4t
    Sue 6 t-2 6(t-2)

    \begin{array}{rrrrr} 4t&=&6(t&-&2) \\ 4t&=&6t&-&12 \\ -6t&&-6t&& \\ \midrule \dfrac{-2t}{-2}&=&\dfrac{-12}{-2}&& \\ \\ t&=&6&& \\ t-2&=&4&& \end{array}

  14. Who or What Rate Time Equation
    M1 5 t 5t
    M2 8 t-6 8(t-6)

    \begin{array}{rrrrr} 5t&=&8(t&-&6) \\ 5t&=&8t&-&48 \\ -8t&&-8t&& \\ \midrule \dfrac{-3t}{-3}&=&\dfrac{-48}{-3}&& \\ \\ t&=&16&& \\ t-6&=&10&& \end{array}

  15. Who or What Rate Time Equation
    MB 8 t 8t
    CC 16 t-2 16(t-2)

    \begin{array}{rrrrr} 8t&=&16(t&-&2) \\ 8t&=&16t&-&32 \\ -16t&&-16t&& \\ \midrule \dfrac{-8t}{-8}&=&\dfrac{-32}{-8}&& \\ \\ t&=&4&& \\ t-2&=&2&& \end{array}

  16. Who or What Rate Time Equation
    R1 6 t 6t
    R2 8 t-1 8(t-1)

    \begin{array}{rrrrr} 6t&=&8(t&-&1) \\ 6t&=&8t&-&8 \\ -8t&&-8t&& \\ \midrule \dfrac{-2t}{-2}&=&\dfrac{-8}{-2}&& \\ \\ t&=&4&& \\ t-1&=&3&& \end{array}

  17. Who or What Rate Time Equation
    M1 20 t 20t
    M2 30 t 30t

    \begin{array}{rrrrl} 20t&+&30t&=&300 \\ \\ &&\dfrac{50t}{50}&=&\dfrac{300}{50} \\ \\ &&t&=&6 \end{array}

  18. Who or What Rate Time Equation
    T1 r 4 4r
    T2 r+6 4 4(r+6)

    \begin{array}{rrrrrrr} 4r&+&4(r&+&6)&=&168 \\ 4r&+&4r&+&24&=&168 \\ &&&-&24&&-24 \\ \midrule &&&&\dfrac{8r}{8}&=&\dfrac{144}{8} \\ \\ &&&&r&=&18 \\ &&&&r+6&=&24 \end{array}

  19. Who or What Rate Time Equation
    C1 r 3 3r
    C2 2r 3 3(2r)

    \begin{array}{rrrrl} 3r&+&3(2r)&=&72 \\ 3r&+&6r&=&72 \\ \\ &&\dfrac{9r}{9}&=&\dfrac{72}{9} \\ \\ &&r&=&8 \\ \\ &&C_1&=&\phantom{0}8\text{ km/h} \\ &&C_2&=&16\text{ km/h} \end{array}

  20. Who or What Rate Time Equation
    P1 r-25 2 2(r-25)
    P2 r 2 2r

    \begin{array}{rrrrrrl} 2(r&-&25)&+&2r&=&430 \\ 2r&-&50&+&2r&=&430 \\ &+&50&&&&+50 \\ \midrule &&&&\dfrac{4r}{4}&=&\dfrac{480}{4} \\ \\ &&&&r&=&120 \\ \\ &&&&P_1&=&120-25=95 \\ &&&&P_2&=&120 \end{array}

  21. Who or What Rate Time Equation
    S1 55 t 55t
    S2 40 2.5-t 40(2.5-t)

    \begin{array}{rrrrrrr} 55t&+&40(2.5&-&t)&=&130 \\ 55t&+&100&-&40t&=&130 \\ &-&100&&&&-100 \\ \midrule &&&&\dfrac{15t}{15}&=&\dfrac{30}{15} \\ \\ &&&&t&=&2 \end{array}

  22. Who or What Rate Time Equation
    To end 8 t 8t
    Return 3 55-t 3(55-t)

    \begin{array}{rrlrr} 8t&=&3(55&-&t) \\ 8t&=&165&-&3t \\ +3t&&&+&3t \\ \midrule \dfrac{11t}{11}&=&\dfrac{165}{11}&& \\ \\ t&=&15&& \\ \\ d&=&r\cdot t&& \\ d&=&8(15)&& \\ d&=&120\text{ m}&& \end{array}

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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