{"id":1952,"date":"2021-12-02T19:40:09","date_gmt":"2021-12-03T00:40:09","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-8-8\/"},"modified":"2022-11-02T10:38:41","modified_gmt":"2022-11-02T14:38:41","slug":"answer-key-8-8","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-8-8\/","title":{"raw":"Answer Key 8.8","rendered":"Answer Key 8.8"},"content":{"raw":"
    \n \t
  1. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    A<\/th>\n[latex]20[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]20t[\/latex]<\/td>\n<\/tr>\n
    B<\/th>\n[latex]25[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]25t[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]20t+25t=60[\/latex]<\/li>\n \t
  2. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    A1<\/sub><\/th>\n[latex]r[\/latex]<\/td>\n[latex]6[\/latex]<\/td>\n[latex]6r[\/latex]<\/td>\n<\/tr>\n
    A1<\/sub><\/th>\n[latex]r+s[\/latex]<\/td>\n[latex]6[\/latex]<\/td>\n[latex]6(r+s)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]6r+6(r+s)=276[\/latex]<\/li>\n \t
  3. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    T1<\/sub><\/th>\n[latex]25[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]25t[\/latex]<\/td>\n<\/tr>\n
    T2<\/sub><\/th>\n[latex]40[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]40t[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]25t+40t=195[\/latex]<\/li>\n \t
  4. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    J<\/th>\n[latex]20[\/latex]<\/td>\n[latex]5[\/latex]<\/td>\n[latex]20(5)[\/latex]<\/td>\n<\/tr>\n
    S<\/th>\n[latex]r[\/latex]<\/td>\n[latex]5[\/latex]<\/td>\n[latex]r(5)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]20(5)+5r=150[\/latex]<\/li>\n \t
  5. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    P<\/th>\n[latex]r+15[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n[latex]4(r+15)[\/latex]<\/td>\n<\/tr>\n
    F<\/th>\n[latex]r[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n[latex]4r[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]4(r+15)+4r=300[\/latex]<\/li>\n \t
  6. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    A1<\/sub><\/th>\n[latex]25[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]25t[\/latex]<\/td>\n<\/tr>\n
    A2<\/sub><\/th>\n[latex]35[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]35t[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]25t+35t=180[\/latex]<\/li>\n \t
  7. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    Away<\/th>\n[latex]10[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]10(t)[\/latex]<\/td>\n<\/tr>\n
    Return<\/th>\n[latex]3[\/latex]<\/td>\n[latex]10-t[\/latex]<\/td>\n[latex]3(10-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]10t=3(10-t)[\/latex]<\/li>\n \t
  8. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    w<\/th>\n[latex]4[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]4t[\/latex]<\/td>\n<\/tr>\n
    r<\/th>\n[latex]20[\/latex]<\/td>\n[latex](3-t)[\/latex]<\/td>\n[latex]20(3-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]4t=20(3-t)[\/latex]<\/li>\n \t
  9. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    Away<\/th>\n[latex]28[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]28t[\/latex]<\/td>\n<\/tr>\n
    Back<\/th>\n[latex]4[\/latex]<\/td>\n[latex]2-t[\/latex]<\/td>\n[latex]4(2-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrlrr}\n28t&=&4(2&-&t) \\\\\n28t&=&8&-&4t \\\\\n+4t&&&+&4t \\\\\n\\hline\n\\dfrac{32t}{32}&=&\\dfrac{8}{32}&& \\\\ \\\\\nt&=&\\dfrac{1}{4}&& \\\\ \\\\\nd&=&rt&& \\\\\nd&=&28(\\dfrac{1}{4})&& \\\\\nd&=&7\\text{ km}&&\n\n\\end{array}[\/latex]<\/li>\n \t
  10. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    Leave<\/th>\n[latex]15[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]15t[\/latex]<\/td>\n<\/tr>\n
    Return<\/th>\n[latex]10[\/latex]<\/td>\n[latex]5-t[\/latex]<\/td>\n[latex]10(5-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrlrr}\n15t&=&10(5&-&t) \\\\\n15t&=&50&-&10t \\\\\n+10t&&&+&10t \\\\\n\\hline\n\\dfrac{25t}{25}&=&\\dfrac{50}{25}&& \\\\ \\\\\nt&=&2&& \\\\ \\\\\nd&=&rt&& \\\\\nd&=&15(2)&& \\\\\nd&=&30\\text{ km}&&\n\\end{array}[\/latex]<\/li>\n \t
  11. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    To resort<\/th>\n[latex]30[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]30t[\/latex]<\/td>\n<\/tr>\n
    Return<\/th>\n[latex]50[\/latex]<\/td>\n[latex]8-t[\/latex]<\/td>\n[latex]50(8-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrlrr}\n30t&=&50(8&-&t) \\\\\n30t&=&400&-&50t \\\\\n+50t&&&+&50t \\\\\n\\hline\n\\dfrac{80t}{80}&=&\\dfrac{400}{80}&& \\\\ \\\\\nt&=&5&& \\\\ \\\\\nd&=&rt&& \\\\\nd&=&30(5)&& \\\\\nd&=&150\\text{ km}&&\n\\end{array}[\/latex]<\/li>\n \t
  12. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    To airport<\/th>\n[latex]90[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]90t[\/latex]<\/td>\n<\/tr>\n
    Return<\/th>\n[latex]120[\/latex]<\/td>\n[latex]7-t[\/latex]<\/td>\n[latex]120(7-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrlrr}\n90t&=&120(7&-&t) \\\\\n90t&=&840&-&120t \\\\\n+120t&&&+&120t \\\\\n\\hline\n\\dfrac{210t}{210}&=&\\dfrac{840}{210}&& \\\\ \\\\\nt&=&4&& \\\\ \\\\\nd&=&rt&& \\\\\nd&=&90(4)&& \\\\\nd&=&360\\text{ km}&&\n\\end{array}[\/latex]<\/li>\n \t
  13. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    Sam<\/th>\n[latex]4[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]4t[\/latex]<\/td>\n<\/tr>\n
    Sue<\/th>\n[latex]6[\/latex]<\/td>\n[latex]t-2[\/latex]<\/td>\n[latex]6(t-2)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrr}\n4t&=&6(t&-&2) \\\\\n4t&=&6t&-&12 \\\\\n-6t&&-6t&& \\\\\n\\hline\n\\dfrac{-2t}{-2}&=&\\dfrac{-12}{-2}&& \\\\ \\\\\nt&=&6&& \\\\\nt-2&=&4&&\n\\end{array}[\/latex]<\/li>\n \t
  14. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    M1<\/sub><\/th>\n[latex]5[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]5t[\/latex]<\/td>\n<\/tr>\n
    M2<\/sub><\/th>\n[latex]8[\/latex]<\/td>\n[latex]t-6[\/latex]<\/td>\n[latex]8(t-6)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrr}\n5t&=&8(t&-&6) \\\\\n5t&=&8t&-&48 \\\\\n-8t&&-8t&& \\\\\n\\hline\n\\dfrac{-3t}{-3}&=&\\dfrac{-48}{-3}&& \\\\ \\\\\nt&=&16&& \\\\\nt-6&=&10&&\n\\end{array}[\/latex]<\/li>\n \t
  15. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    MB<\/th>\n[latex]8[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]8t[\/latex]<\/td>\n<\/tr>\n
    CC<\/th>\n[latex]16[\/latex]<\/td>\n[latex]t-2[\/latex]<\/td>\n[latex]16(t-2)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrr}\n8t&=&16(t&-&2) \\\\\n8t&=&16t&-&32 \\\\\n-16t&&-16t&& \\\\\n\\hline\n\\dfrac{-8t}{-8}&=&\\dfrac{-32}{-8}&& \\\\ \\\\\nt&=&4&& \\\\\nt-2&=&2&&\n\\end{array}[\/latex]<\/li>\n \t
  16. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    R1<\/sub><\/th>\n[latex]6[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]6t[\/latex]<\/td>\n<\/tr>\n
    R2<\/sub><\/th>\n[latex]8[\/latex]<\/td>\n[latex]t-1[\/latex]<\/td>\n[latex]8(t-1)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrr}\n6t&=&8(t&-&1) \\\\\n6t&=&8t&-&8 \\\\\n-8t&&-8t&& \\\\\n\\hline\n\\dfrac{-2t}{-2}&=&\\dfrac{-8}{-2}&& \\\\ \\\\\nt&=&4&& \\\\\nt-1&=&3&&\n\\end{array}[\/latex]<\/li>\n \t
  17. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    M1<\/sub><\/th>\n[latex]20[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]20t[\/latex]<\/td>\n<\/tr>\n
    M2<\/sub><\/th>\n[latex]30[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]30t[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrl}\n20t&+&30t&=&300 \\\\ \\\\\n&&\\dfrac{50t}{50}&=&\\dfrac{300}{50} \\\\ \\\\\n&&t&=&6\n\\end{array}[\/latex]<\/li>\n \t
  18. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    T1<\/sub><\/th>\n[latex]r[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n[latex]4r[\/latex]<\/td>\n<\/tr>\n
    T2<\/sub><\/th>\n[latex]r+6[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n[latex]4(r+6)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrr}\n4r&+&4(r&+&6)&=&168 \\\\\n4r&+&4r&+&24&=&168 \\\\\n&&&-&24&&-24 \\\\\n\\hline\n&&&&\\dfrac{8r}{8}&=&\\dfrac{144}{8} \\\\ \\\\\n&&&&r&=&18 \\\\\n&&&&r+6&=&24\n\\end{array}[\/latex]<\/li>\n \t
  19. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    C1<\/sub><\/th>\n[latex]r[\/latex]<\/td>\n[latex]3[\/latex]<\/td>\n[latex]3r[\/latex]<\/td>\n<\/tr>\n
    C2<\/sub><\/th>\n[latex]2r[\/latex]<\/td>\n[latex]3[\/latex]<\/td>\n[latex]3(2r)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrl}\n3r&+&3(2r)&=&72 \\\\\n3r&+&6r&=&72 \\\\ \\\\\n&&\\dfrac{9r}{9}&=&\\dfrac{72}{9} \\\\ \\\\\n&&r&=&8 \\\\ \\\\\n&&C_1&=&\\phantom{0}8\\text{ km\/h} \\\\\n&&C_2&=&16\\text{ km\/h}\n\\end{array}[\/latex]<\/li>\n \t
  20. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    P1<\/sub><\/th>\n[latex]r-25[\/latex]<\/td>\n[latex]2[\/latex]<\/td>\n[latex]2(r-25)[\/latex]<\/td>\n<\/tr>\n
    P2<\/sub><\/th>\n[latex]r[\/latex]<\/td>\n[latex]2[\/latex]<\/td>\n[latex]2r[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrl}\n2(r&-&25)&+&2r&=&430 \\\\\n2r&-&50&+&2r&=&430 \\\\\n&+&50&&&&+50 \\\\\n\\hline\n&&&&\\dfrac{4r}{4}&=&\\dfrac{480}{4} \\\\ \\\\\n&&&&r&=&120 \\\\ \\\\\n&&&&P_1&=&120-25=95 \\\\\n&&&&P_2&=&120\n\\end{array}[\/latex]<\/li>\n \t
  21. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    S1<\/sub><\/th>\n[latex]55[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]55t[\/latex]<\/td>\n<\/tr>\n
    S2<\/sub><\/th>\n[latex]40[\/latex]<\/td>\n[latex]2.5-t[\/latex]<\/td>\n[latex]40(2.5-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrr}\n55t&+&40(2.5&-&t)&=&130 \\\\\n55t&+&100&-&40t&=&130 \\\\\n&-&100&&&&-100 \\\\\n\\hline\n&&&&\\dfrac{15t}{15}&=&\\dfrac{30}{15} \\\\ \\\\\n&&&&t&=&2\n\\end{array}[\/latex]<\/li>\n \t
  22. \n\n\n\n\n\n
    Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
    To end<\/th>\n[latex]8[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]8t[\/latex]<\/td>\n<\/tr>\n
    Return<\/th>\n[latex]3[\/latex]<\/td>\n[latex]55-t[\/latex]<\/td>\n[latex]3(55-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrlrr}\n8t&=&3(55&-&t) \\\\\n8t&=&165&-&3t \\\\\n+3t&&&+&3t \\\\\n\\hline\n\\dfrac{11t}{11}&=&\\dfrac{165}{11}&& \\\\ \\\\\nt&=&15&& \\\\ \\\\\nd&=&r\\cdot t&& \\\\\nd&=&8(15)&& \\\\\nd&=&120\\text{ m}&&\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      A<\/th>\n[latex]20[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]20t[\/latex]<\/td>\n<\/tr>\n
      B<\/th>\n[latex]25[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]25t[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]20t+25t=60[\/latex]<\/li>\n

    2. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      A1<\/sub><\/th>\n[latex]r[\/latex]<\/td>\n[latex]6[\/latex]<\/td>\n[latex]6r[\/latex]<\/td>\n<\/tr>\n
      A1<\/sub><\/th>\n[latex]r+s[\/latex]<\/td>\n[latex]6[\/latex]<\/td>\n[latex]6(r+s)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]6r+6(r+s)=276[\/latex]<\/li>\n

    3. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      T1<\/sub><\/th>\n[latex]25[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]25t[\/latex]<\/td>\n<\/tr>\n
      T2<\/sub><\/th>\n[latex]40[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]40t[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]25t+40t=195[\/latex]<\/li>\n

    4. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      J<\/th>\n[latex]20[\/latex]<\/td>\n[latex]5[\/latex]<\/td>\n[latex]20(5)[\/latex]<\/td>\n<\/tr>\n
      S<\/th>\n[latex]r[\/latex]<\/td>\n[latex]5[\/latex]<\/td>\n[latex]r(5)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]20(5)+5r=150[\/latex]<\/li>\n

    5. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      P<\/th>\n[latex]r+15[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n[latex]4(r+15)[\/latex]<\/td>\n<\/tr>\n
      F<\/th>\n[latex]r[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n[latex]4r[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]4(r+15)+4r=300[\/latex]<\/li>\n

    6. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      A1<\/sub><\/th>\n[latex]25[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]25t[\/latex]<\/td>\n<\/tr>\n
      A2<\/sub><\/th>\n[latex]35[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]35t[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]25t+35t=180[\/latex]<\/li>\n

    7. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      Away<\/th>\n[latex]10[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]10(t)[\/latex]<\/td>\n<\/tr>\n
      Return<\/th>\n[latex]3[\/latex]<\/td>\n[latex]10-t[\/latex]<\/td>\n[latex]3(10-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]10t=3(10-t)[\/latex]<\/li>\n

    8. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      w<\/th>\n[latex]4[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]4t[\/latex]<\/td>\n<\/tr>\n
      r<\/th>\n[latex]20[\/latex]<\/td>\n[latex](3-t)[\/latex]<\/td>\n[latex]20(3-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]4t=20(3-t)[\/latex]<\/li>\n

    9. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      Away<\/th>\n[latex]28[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]28t[\/latex]<\/td>\n<\/tr>\n
      Back<\/th>\n[latex]4[\/latex]<\/td>\n[latex]2-t[\/latex]<\/td>\n[latex]4(2-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    10. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      Leave<\/th>\n[latex]15[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]15t[\/latex]<\/td>\n<\/tr>\n
      Return<\/th>\n[latex]10[\/latex]<\/td>\n[latex]5-t[\/latex]<\/td>\n[latex]10(5-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    11. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      To resort<\/th>\n[latex]30[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]30t[\/latex]<\/td>\n<\/tr>\n
      Return<\/th>\n[latex]50[\/latex]<\/td>\n[latex]8-t[\/latex]<\/td>\n[latex]50(8-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    12. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      To airport<\/th>\n[latex]90[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]90t[\/latex]<\/td>\n<\/tr>\n
      Return<\/th>\n[latex]120[\/latex]<\/td>\n[latex]7-t[\/latex]<\/td>\n[latex]120(7-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    13. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      Sam<\/th>\n[latex]4[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]4t[\/latex]<\/td>\n<\/tr>\n
      Sue<\/th>\n[latex]6[\/latex]<\/td>\n[latex]t-2[\/latex]<\/td>\n[latex]6(t-2)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    14. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      M1<\/sub><\/th>\n[latex]5[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]5t[\/latex]<\/td>\n<\/tr>\n
      M2<\/sub><\/th>\n[latex]8[\/latex]<\/td>\n[latex]t-6[\/latex]<\/td>\n[latex]8(t-6)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    15. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      MB<\/th>\n[latex]8[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]8t[\/latex]<\/td>\n<\/tr>\n
      CC<\/th>\n[latex]16[\/latex]<\/td>\n[latex]t-2[\/latex]<\/td>\n[latex]16(t-2)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    16. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      R1<\/sub><\/th>\n[latex]6[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]6t[\/latex]<\/td>\n<\/tr>\n
      R2<\/sub><\/th>\n[latex]8[\/latex]<\/td>\n[latex]t-1[\/latex]<\/td>\n[latex]8(t-1)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    17. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      M1<\/sub><\/th>\n[latex]20[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]20t[\/latex]<\/td>\n<\/tr>\n
      M2<\/sub><\/th>\n[latex]30[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]30t[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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

    18. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      T1<\/sub><\/th>\n[latex]r[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n[latex]4r[\/latex]<\/td>\n<\/tr>\n
      T2<\/sub><\/th>\n[latex]r+6[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n[latex]4(r+6)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    19. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      C1<\/sub><\/th>\n[latex]r[\/latex]<\/td>\n[latex]3[\/latex]<\/td>\n[latex]3r[\/latex]<\/td>\n<\/tr>\n
      C2<\/sub><\/th>\n[latex]2r[\/latex]<\/td>\n[latex]3[\/latex]<\/td>\n[latex]3(2r)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    20. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      P1<\/sub><\/th>\n[latex]r-25[\/latex]<\/td>\n[latex]2[\/latex]<\/td>\n[latex]2(r-25)[\/latex]<\/td>\n<\/tr>\n
      P2<\/sub><\/th>\n[latex]r[\/latex]<\/td>\n[latex]2[\/latex]<\/td>\n[latex]2r[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    21. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      S1<\/sub><\/th>\n[latex]55[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]55t[\/latex]<\/td>\n<\/tr>\n
      S2<\/sub><\/th>\n[latex]40[\/latex]<\/td>\n[latex]2.5-t[\/latex]<\/td>\n[latex]40(2.5-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n

    22. \n\n\n\n\n\n
      Who or What<\/th>\nRate<\/th>\nTime<\/th>\nEquation<\/th>\n<\/tr>\n
      To end<\/th>\n[latex]8[\/latex]<\/td>\n[latex]t[\/latex]<\/td>\n[latex]8t[\/latex]<\/td>\n<\/tr>\n
      Return<\/th>\n[latex]3[\/latex]<\/td>\n[latex]55-t[\/latex]<\/td>\n[latex]3(55-t)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [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]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":81,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1952","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1952","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1952\/revisions"}],"predecessor-version":[{"id":1953,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1952\/revisions\/1953"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1952\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1952"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1952"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1952"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1952"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}