Answer Key 8.8

  1. Who or What Rate Time Equation
    A [latex]20[/latex] [latex]t[/latex] [latex]20t[/latex]
    B [latex]25[/latex] [latex]t[/latex] [latex]25t[/latex]

    [latex]20t+25t=60[/latex]

  2. Who or What Rate Time Equation
    A1 [latex]r[/latex] [latex]6[/latex] [latex]6r[/latex]
    A1 [latex]r+s[/latex] [latex]6[/latex] [latex]6(r+s)[/latex]

    [latex]6r+6(r+s)=276[/latex]

  3. Who or What Rate Time Equation
    T1 [latex]25[/latex] [latex]t[/latex] [latex]25t[/latex]
    T2 [latex]40[/latex] [latex]t[/latex] [latex]40t[/latex]

    [latex]25t+40t=195[/latex]

  4. Who or What Rate Time Equation
    J [latex]20[/latex] [latex]5[/latex] [latex]20(5)[/latex]
    S [latex]r[/latex] [latex]5[/latex] [latex]r(5)[/latex]

    [latex]20(5)+5r=150[/latex]

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

    [latex]4(r+15)+4r=300[/latex]

  6. Who or What Rate Time Equation
    A1 [latex]25[/latex] [latex]t[/latex] [latex]25t[/latex]
    A2 [latex]35[/latex] [latex]t[/latex] [latex]35t[/latex]

    [latex]25t+35t=180[/latex]

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

    [latex]10t=3(10-t)[/latex]

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

    [latex]4t=20(3-t)[/latex]

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

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

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

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

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

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

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

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

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

    [latex]\begin{array}{rrrrr} 4t&=&6(t&-&2) \\ 4t&=&6t&-&12 \\ -6t&&-6t&& \\ \hline \dfrac{-2t}{-2}&=&\dfrac{-12}{-2}&& \\ \\ t&=&6&& \\ t-2&=&4&& \end{array}[/latex]

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

    [latex]\begin{array}{rrrrr} 5t&=&8(t&-&6) \\ 5t&=&8t&-&48 \\ -8t&&-8t&& \\ \hline \dfrac{-3t}{-3}&=&\dfrac{-48}{-3}&& \\ \\ t&=&16&& \\ t-6&=&10&& \end{array}[/latex]

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

    [latex]\begin{array}{rrrrr} 8t&=&16(t&-&2) \\ 8t&=&16t&-&32 \\ -16t&&-16t&& \\ \hline \dfrac{-8t}{-8}&=&\dfrac{-32}{-8}&& \\ \\ t&=&4&& \\ t-2&=&2&& \end{array}[/latex]

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

    [latex]\begin{array}{rrrrr} 6t&=&8(t&-&1) \\ 6t&=&8t&-&8 \\ -8t&&-8t&& \\ \hline \dfrac{-2t}{-2}&=&\dfrac{-8}{-2}&& \\ \\ t&=&4&& \\ t-1&=&3&& \end{array}[/latex]

  17. Who or What Rate Time Equation
    M1 [latex]20[/latex] [latex]t[/latex] [latex]20t[/latex]
    M2 [latex]30[/latex] [latex]t[/latex] [latex]30t[/latex]

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

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

    [latex]\begin{array}{rrrrrrr} 4r&+&4(r&+&6)&=&168 \\ 4r&+&4r&+&24&=&168 \\ &&&-&24&&-24 \\ \hline &&&&\dfrac{8r}{8}&=&\dfrac{144}{8} \\ \\ &&&&r&=&18 \\ &&&&r+6&=&24 \end{array}[/latex]

  19. Who or What Rate Time Equation
    C1 [latex]r[/latex] [latex]3[/latex] [latex]3r[/latex]
    C2 [latex]2r[/latex] [latex]3[/latex] [latex]3(2r)[/latex]

    [latex]\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}[/latex]

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

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

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

    [latex]\begin{array}{rrrrrrr} 55t&+&40(2.5&-&t)&=&130 \\ 55t&+&100&-&40t&=&130 \\ &-&100&&&&-100 \\ \hline &&&&\dfrac{15t}{15}&=&\dfrac{30}{15} \\ \\ &&&&t&=&2 \end{array}[/latex]

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

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

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Intermediate Algebra (Convert to MathJax) Copyright © 2020 by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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