{"id":1972,"date":"2021-12-02T19:40:15","date_gmt":"2021-12-03T00:40:15","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-9-10\/"},"modified":"2023-11-01T16:18:24","modified_gmt":"2023-11-01T20:18:24","slug":"answer-key-9-10","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-9-10\/","title":{"raw":"Answer Key 9.10","rendered":"Answer Key 9.10"},"content":{"raw":"
    \r\n \t
  1. [latex]\\text{Father}=\\text{Bill}-2\\text{ h}[\/latex]\r\n[latex]\\therefore \\dfrac{1}{B-2\\text{ h}}+\\dfrac{1}{B}=\\dfrac{1}{2\\text{ h } 24\\text{ min}}[\/latex]<\/li>\r\n \t
  2. [latex]\\text{Smaller}=\\text{Larger}+4\\text{ h}[\/latex]\r\n[latex]\\therefore \\dfrac{1}{L+4\\text{ h}}+\\dfrac{1}{L}=\\dfrac{1}{3\\text{ h }45\\text{ min}}[\/latex]<\/li>\r\n \t
  3. [latex]\\text{Jack}=\\text{Bob}-1\\text{ h}[\/latex]\r\n[latex]\\therefore \\dfrac{1}{B-1\\text{ h}}+\\dfrac{1}{B}=\\dfrac{1}{1.2\\text{ h}}[\/latex]<\/li>\r\n \t
  4. [latex]\\dfrac{1}{Y}+\\dfrac{1}{B}=\\dfrac{1}{T}[\/latex]\r\n[latex]\\begin{array}{l}Y=6\\text{ d}\\\\\r\nB=4\\text{ d}\\\\ \\\\\r\n\\therefore \\dfrac{1}{6}+\\dfrac{1}{4}=\\dfrac{1}{T}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  5. [latex]\\text{John}=\\text{Carlos}+8\\text{ h}[\/latex]\r\n[latex]\\dfrac{1}{C+8\\text{ h}}+\\dfrac{1}{C}=\\dfrac{1}{3\\text{ h}}[\/latex]<\/li>\r\n \t
  6. [latex]M=3\\text{ d}[\/latex]\r\n[latex]N=4\\text{ d}[\/latex]\r\n[latex]E=5\\text{ d}[\/latex]\r\n[latex]\\begin{array}[t]{l}\r\n\\dfrac{1}{M}+\\dfrac{1}{N}+\\dfrac{1}{E}=\\dfrac{1}{T} \\\\ \\\\\r\n\\dfrac{1}{3\\text{ d}}+\\dfrac{1}{4\\text{ d}}+\\dfrac{1}{5\\text{ d}}=\\dfrac{1}{T}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  7. [latex]\\text{Raj}=4 \\text{ d}[\/latex]\r\n[latex]\\begin{array}[t]{l}\r\n\\text{Rubi}=\\dfrac{1}{2}\\text{ Raj or }2\\text{ d} \\\\ \\\\\r\n\\therefore \\dfrac{1}{4 \\text{ d}}+\\dfrac{1}{2\\text{ d}}=\\dfrac{1}{T}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  8. [latex]\\dfrac{1}{20\\text{ min}}+\\dfrac{1}{30\\text{ min}}=\\dfrac{1}{T}[\/latex]<\/li>\r\n \t
  9. [latex]\\dfrac{1}{24\\text{ d}}+\\dfrac{1}{I}=\\dfrac{1}{6\\text{ d}}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrl}\r\n&&\\dfrac{1}{I}&=&\\dfrac{1}{6\\text{ d}}-\\dfrac{1}{24\\text{ d}} \\\\ \\\\\r\n&&\\dfrac{1}{I}&=&\\dfrac{4}{24\\text{ d}}-\\dfrac{1}{24\\text{ d}} \\\\ \\\\\r\n&&\\dfrac{1}{I}&=&\\dfrac{1}{8\\text{ d}} \\\\ \\\\\r\n&&\\therefore I&=&8\\text{ days}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  10. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrl}\r\n\\dfrac{1}{C}&+&\\dfrac{1}{A}&=&\\dfrac{1}{3.75\\text{ d}}\r\n\\dfrac{1}{5\\text{ d}}&+&\\dfrac{1}{A}&=&\\dfrac{1}{3.75\\text{ d}} \\\\ \\\\\r\n&&\\dfrac{1}{A}&=&\\dfrac{1}{3.75\\text{ d}}-\\dfrac{1}{5\\text{ d}} \\\\ \\\\\r\n&&\\dfrac{1}{A}&=&\\dfrac{4}{15\\text{ d}}-\\dfrac{3}{15\\text{ d}} \\\\ \\\\\r\n&&\\dfrac{1}{A}&=&\\dfrac{1}{15\\text{ d}} \\\\ \\\\\r\n&&\\therefore A&=&15\\text{ days}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  11. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrl}\r\n\\dfrac{1}{S}&+&\\dfrac{1}{F}&=&\\dfrac{1}{\\text{job}}\r\n\\dfrac{1}{3\\text{ d}}&+&\\dfrac{1}{6\\text{ d}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\\r\n\\dfrac{2}{6\\text{ d}}&+&\\dfrac{1}{6\\text{ d}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\\r\n&&\\dfrac{3}{6\\text{ d}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\\r\n&&\\dfrac{1}{2\\text{ d}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\\r\n&&\\therefore \\text{job}&=&2 \\text{ days}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  12. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrl}\r\n\\dfrac{1}{T}&+&\\dfrac{1}{J}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\\r\n\\dfrac{1}{10\\text{ h}}&+&\\dfrac{1}{8\\text{ h}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\\r\n\\dfrac{4}{40\\text{ h}}&+&\\dfrac{5}{40\\text{ h}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\\r\n&&\\dfrac{9}{40\\text{ h}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\\r\n&&\\therefore \\text{job}&=&\\dfrac{40\\text{ h}}{9} \\\\ \\\\\r\n&&\\text{job}&=&4\\dfrac{4}{9}\\text{ h}= 4.\\bar{4}\\text{ h}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  13. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrl}\r\n&&\\text{slow}&=&2\\times \\text{fast} \\\\ \\\\\r\n&&\\dfrac{1}{2}\\text{slow}&=& \\text{fast}\\\\ \\\\\r\n\\dfrac{1}{F}&+&\\dfrac{1}{S}&=&\\dfrac{1}{6\\text{ h}} \\\\ \\\\\r\n\\dfrac{1}{\\dfrac{1}{2}S}&+&\\dfrac{1}{S}&=&\\dfrac{1}{6\\text{ h}} \\\\ \\\\\r\n\\left(\\dfrac{2}{2}\\right)\\dfrac{1}{\\dfrac{1}{2}S}&+&\\dfrac{1}{S}&=&\\dfrac{1}{6\\text{ h}} \\\\ \\\\\r\n\\dfrac{2}{S}&+&\\dfrac{1}{S}&=&\\dfrac{1}{6\\text{ h}} \\\\ \\\\\r\n&&\\dfrac{3}{S}&=&\\dfrac{1}{6\\text{ h}} \\\\ \\\\\r\n&&\\dfrac{S}{3}&=&6\\text{ h} \\\\ \\\\\r\n&&S&=&6(3) \\\\ \\\\\r\n&&S&=&18\\text{ h}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  14. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrl}\r\n&&\\text{slower}&=&3\\times \\text{faster} \\\\ \\\\\r\n\\dfrac{1}{F}&+&\\dfrac{1}{S}&=&\\dfrac{1}{3\\text{ h}} \\\\ \\\\\r\n\\dfrac{1}{F}&+&\\dfrac{1}{3F}&=&\\dfrac{1}{3\\text{ h}} \\\\ \\\\\r\n\\dfrac{3}{3F}&+&\\dfrac{1}{3F}&=&\\dfrac{1}{3\\text{ h}} \\\\ \\\\\r\n&&\\dfrac{4}{3F}&=&\\dfrac{1}{3\\text{ h}} \\\\ \\\\\r\n&&\\therefore \\dfrac{4}{3}&=&\\dfrac{F}{3\\text{ h}} \\\\ \\\\\r\n&&F&=&4\\text{ h}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  15. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrl}\r\n&&\\text{full}&=&8\\text{ h} \\\\ \\\\\r\n&&\\text{empty}&=&2\\times\\text{full or }16\\text{ h} \\\\ \\\\\r\n\\dfrac{1}{F}&-&\\dfrac{1}{E}&=&\\dfrac{1}{T} \\\\ \\\\\r\n\\dfrac{1}{8\\text{ h}}&-&\\dfrac{1}{16\\text{ h}}&=&\\dfrac{1}{T} \\\\ \\\\\r\n\\dfrac{2}{16\\text{ h}}&-&\\dfrac{1}{16\\text{ h}}&=&\\dfrac{1}{T} \\\\ \\\\\r\n&&\\therefore \\dfrac{1}{16\\text{ h}}&=&\\dfrac{1}{T} \\\\ \\\\\r\n&&T&=&16\\text{ h}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  16. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrl}\r\n\\dfrac{1}{E}&-&\\dfrac{1}{F}&=&\\dfrac{1}{T} \\\\ \\\\\r\n\\dfrac{1}{3}&-&\\dfrac{1}{5}&=&\\dfrac{1}{T} \\\\ \\\\\r\n\\dfrac{5}{15}&-&\\dfrac{3}{15}&=&\\dfrac{1}{T} \\\\ \\\\\r\n&&\\dfrac{2}{15\\text{ min}}&=&\\dfrac{1}{T} \\\\ \\\\\r\n&&\\therefore T&=&\\dfrac{15\\text{ min}}{2}=7.5\\text{ min}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  17. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrl}\r\n\\dfrac{1}{\\text{full}}&-&\\dfrac{1}{\\text{empty}}&=&\\dfrac{1}{2 T} \\\\ \\\\\r\n\\dfrac{1}{10\\text{ h}}&-&\\dfrac{1}{15\\text{ h}}&=&\\dfrac{1}{2 T} \\\\ \\\\\r\n\\dfrac{3}{30\\text{ h}}&-&\\dfrac{2}{30\\text{ h}}&=&\\dfrac{1}{2 T} \\\\ \\\\\r\n&&\\dfrac{1}{30\\text{ h}}&=&\\dfrac{1}{2 T} \\\\ \\\\\r\n&&2T&=&30\\text{ h} \\\\ \\\\\r\n&&T&=&\\dfrac{30\\text{ h}}{2} \\\\ \\\\\r\n&&T&=&15\\text{ h}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  18. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrl}\r\n\\dfrac{1}{\\text{full}}&-&\\dfrac{1}{\\text{empty}}&=&\\dfrac{3}{4T} \\\\ \\\\\r\n\\dfrac{1}{6\\text{ min}}&-&\\dfrac{1}{8\\text{ min}}&=&\\dfrac{3}{4T} \\\\ \\\\\r\n\\dfrac{4}{24\\text{ min}}&-&\\dfrac{3}{24\\text{ min}}&=&\\dfrac{3}{4T} \\\\ \\\\\r\n&&\\therefore \\dfrac{1}{24\\text{ min}}&=&\\dfrac{3}{4T} \\\\ \\\\\r\n&&T&=&\\dfrac{3}{4}(24\\text{ min}) \\\\ \\\\\r\n&&T&=&18\\text{ min}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  19. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrl}\r\n\\dfrac{1}{H}&+&\\dfrac{1}{C}&=&\\dfrac{1}{T} \\\\ \\\\\r\n\\dfrac{1}{H}&+&\\dfrac{1}{3.5\\text{ min}}&=&\\dfrac{1}{2.1\\text{ min}} \\\\ \\\\\r\n&&\\dfrac{1}{H}&=&\\dfrac{1}{2.1\\text{ min}}-\\dfrac{1}{3.5\\text{ min}} \\\\ \\\\\r\n&&\\dfrac{1}{H}&=&\\dfrac{50}{105\\text{ min}}-\\dfrac{30}{105\\text{ min}} \\\\ \\\\\r\n&&\\dfrac{1}{H}&=&\\dfrac{20}{105\\text{ min}} \\\\ \\\\\r\n&&\\dfrac{1}{H}&=&\\dfrac{4}{21\\text{ min}} \\\\ \\\\\r\n&&H&=&\\dfrac{21}{4}\\text{ min} \\\\ \\\\\r\n&&H&=&5.25 \\text{ min}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  20. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrl}\r\n\\dfrac{1}{A}&+&\\dfrac{1}{B}&=&\\dfrac{1}{T} \\\\ \\\\\r\n\\dfrac{1}{4.5\\text{ h}}&+&\\dfrac{1}{B}&=&\\dfrac{1}{2\\text{ h}} \\\\ \\\\\r\n&&\\dfrac{1}{B}&=&\\dfrac{1}{2\\text{ h}}-\\dfrac{1}{4.5\\text{ h}} \\\\ \\\\\r\n&&\\dfrac{1}{B}&=&\\dfrac{9}{18\\text{ h}}-\\dfrac{4}{18\\text{ h}} \\\\ \\\\\r\n&&\\dfrac{1}{B}&=&\\dfrac{5}{18\\text{ h}} \\\\ \\\\\r\n&&B&=&\\dfrac{18\\text{ h}}{5} \\\\ \\\\\r\n&&B&=&3.6\\text{ h}\r\n\\end{array}[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]\\text{Father}=\\text{Bill}-2\\text{ h}[\/latex]
      \n[latex]\\therefore \\dfrac{1}{B-2\\text{ h}}+\\dfrac{1}{B}=\\dfrac{1}{2\\text{ h } 24\\text{ min}}[\/latex]<\/li>\n
    2. [latex]\\text{Smaller}=\\text{Larger}+4\\text{ h}[\/latex]
      \n[latex]\\therefore \\dfrac{1}{L+4\\text{ h}}+\\dfrac{1}{L}=\\dfrac{1}{3\\text{ h }45\\text{ min}}[\/latex]<\/li>\n
    3. [latex]\\text{Jack}=\\text{Bob}-1\\text{ h}[\/latex]
      \n[latex]\\therefore \\dfrac{1}{B-1\\text{ h}}+\\dfrac{1}{B}=\\dfrac{1}{1.2\\text{ h}}[\/latex]<\/li>\n
    4. [latex]\\dfrac{1}{Y}+\\dfrac{1}{B}=\\dfrac{1}{T}[\/latex]
      \n[latex]\\begin{array}{l}Y=6\\text{ d}\\\\ B=4\\text{ d}\\\\ \\\\ \\therefore \\dfrac{1}{6}+\\dfrac{1}{4}=\\dfrac{1}{T} \\end{array}[\/latex]<\/li>\n
    5. [latex]\\text{John}=\\text{Carlos}+8\\text{ h}[\/latex]
      \n[latex]\\dfrac{1}{C+8\\text{ h}}+\\dfrac{1}{C}=\\dfrac{1}{3\\text{ h}}[\/latex]<\/li>\n
    6. [latex]M=3\\text{ d}[\/latex]
      \n[latex]N=4\\text{ d}[\/latex]
      \n[latex]E=5\\text{ d}[\/latex]
      \n[latex]\\begin{array}[t]{l} \\dfrac{1}{M}+\\dfrac{1}{N}+\\dfrac{1}{E}=\\dfrac{1}{T} \\\\ \\\\ \\dfrac{1}{3\\text{ d}}+\\dfrac{1}{4\\text{ d}}+\\dfrac{1}{5\\text{ d}}=\\dfrac{1}{T} \\end{array}[\/latex]<\/li>\n
    7. [latex]\\text{Raj}=4 \\text{ d}[\/latex]
      \n[latex]\\begin{array}[t]{l} \\text{Rubi}=\\dfrac{1}{2}\\text{ Raj or }2\\text{ d} \\\\ \\\\ \\therefore \\dfrac{1}{4 \\text{ d}}+\\dfrac{1}{2\\text{ d}}=\\dfrac{1}{T} \\end{array}[\/latex]<\/li>\n
    8. [latex]\\dfrac{1}{20\\text{ min}}+\\dfrac{1}{30\\text{ min}}=\\dfrac{1}{T}[\/latex]<\/li>\n
    9. [latex]\\dfrac{1}{24\\text{ d}}+\\dfrac{1}{I}=\\dfrac{1}{6\\text{ d}}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} &&\\dfrac{1}{I}&=&\\dfrac{1}{6\\text{ d}}-\\dfrac{1}{24\\text{ d}} \\\\ \\\\ &&\\dfrac{1}{I}&=&\\dfrac{4}{24\\text{ d}}-\\dfrac{1}{24\\text{ d}} \\\\ \\\\ &&\\dfrac{1}{I}&=&\\dfrac{1}{8\\text{ d}} \\\\ \\\\ &&\\therefore I&=&8\\text{ days} \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} \\dfrac{1}{C}&+&\\dfrac{1}{A}&=&\\dfrac{1}{3.75\\text{ d}} \\dfrac{1}{5\\text{ d}}&+&\\dfrac{1}{A}&=&\\dfrac{1}{3.75\\text{ d}} \\\\ \\\\ &&\\dfrac{1}{A}&=&\\dfrac{1}{3.75\\text{ d}}-\\dfrac{1}{5\\text{ d}} \\\\ \\\\ &&\\dfrac{1}{A}&=&\\dfrac{4}{15\\text{ d}}-\\dfrac{3}{15\\text{ d}} \\\\ \\\\ &&\\dfrac{1}{A}&=&\\dfrac{1}{15\\text{ d}} \\\\ \\\\ &&\\therefore A&=&15\\text{ days} \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} \\dfrac{1}{S}&+&\\dfrac{1}{F}&=&\\dfrac{1}{\\text{job}} \\dfrac{1}{3\\text{ d}}&+&\\dfrac{1}{6\\text{ d}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\ \\dfrac{2}{6\\text{ d}}&+&\\dfrac{1}{6\\text{ d}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\ &&\\dfrac{3}{6\\text{ d}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\ &&\\dfrac{1}{2\\text{ d}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\ &&\\therefore \\text{job}&=&2 \\text{ days} \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} \\dfrac{1}{T}&+&\\dfrac{1}{J}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\ \\dfrac{1}{10\\text{ h}}&+&\\dfrac{1}{8\\text{ h}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\ \\dfrac{4}{40\\text{ h}}&+&\\dfrac{5}{40\\text{ h}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\ &&\\dfrac{9}{40\\text{ h}}&=&\\dfrac{1}{\\text{job}} \\\\ \\\\ &&\\therefore \\text{job}&=&\\dfrac{40\\text{ h}}{9} \\\\ \\\\ &&\\text{job}&=&4\\dfrac{4}{9}\\text{ h}= 4.\\bar{4}\\text{ h} \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} &&\\text{slow}&=&2\\times \\text{fast} \\\\ \\\\ &&\\dfrac{1}{2}\\text{slow}&=& \\text{fast}\\\\ \\\\ \\dfrac{1}{F}&+&\\dfrac{1}{S}&=&\\dfrac{1}{6\\text{ h}} \\\\ \\\\ \\dfrac{1}{\\dfrac{1}{2}S}&+&\\dfrac{1}{S}&=&\\dfrac{1}{6\\text{ h}} \\\\ \\\\ \\left(\\dfrac{2}{2}\\right)\\dfrac{1}{\\dfrac{1}{2}S}&+&\\dfrac{1}{S}&=&\\dfrac{1}{6\\text{ h}} \\\\ \\\\ \\dfrac{2}{S}&+&\\dfrac{1}{S}&=&\\dfrac{1}{6\\text{ h}} \\\\ \\\\ &&\\dfrac{3}{S}&=&\\dfrac{1}{6\\text{ h}} \\\\ \\\\ &&\\dfrac{S}{3}&=&6\\text{ h} \\\\ \\\\ &&S&=&6(3) \\\\ \\\\ &&S&=&18\\text{ h} \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrcrl} &&\\text{slower}&=&3\\times \\text{faster} \\\\ \\\\ \\dfrac{1}{F}&+&\\dfrac{1}{S}&=&\\dfrac{1}{3\\text{ h}} \\\\ \\\\ \\dfrac{1}{F}&+&\\dfrac{1}{3F}&=&\\dfrac{1}{3\\text{ h}} \\\\ \\\\ \\dfrac{3}{3F}&+&\\dfrac{1}{3F}&=&\\dfrac{1}{3\\text{ h}} \\\\ \\\\ &&\\dfrac{4}{3F}&=&\\dfrac{1}{3\\text{ h}} \\\\ \\\\ &&\\therefore \\dfrac{4}{3}&=&\\dfrac{F}{3\\text{ h}} \\\\ \\\\ &&F&=&4\\text{ h} \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrcrl} &&\\text{full}&=&8\\text{ h} \\\\ \\\\ &&\\text{empty}&=&2\\times\\text{full or }16\\text{ h} \\\\ \\\\ \\dfrac{1}{F}&-&\\dfrac{1}{E}&=&\\dfrac{1}{T} \\\\ \\\\ \\dfrac{1}{8\\text{ h}}&-&\\dfrac{1}{16\\text{ h}}&=&\\dfrac{1}{T} \\\\ \\\\ \\dfrac{2}{16\\text{ h}}&-&\\dfrac{1}{16\\text{ h}}&=&\\dfrac{1}{T} \\\\ \\\\ &&\\therefore \\dfrac{1}{16\\text{ h}}&=&\\dfrac{1}{T} \\\\ \\\\ &&T&=&16\\text{ h} \\end{array}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrcrl} \\dfrac{1}{E}&-&\\dfrac{1}{F}&=&\\dfrac{1}{T} \\\\ \\\\ \\dfrac{1}{3}&-&\\dfrac{1}{5}&=&\\dfrac{1}{T} \\\\ \\\\ \\dfrac{5}{15}&-&\\dfrac{3}{15}&=&\\dfrac{1}{T} \\\\ \\\\ &&\\dfrac{2}{15\\text{ min}}&=&\\dfrac{1}{T} \\\\ \\\\ &&\\therefore T&=&\\dfrac{15\\text{ min}}{2}=7.5\\text{ min} \\end{array}[\/latex]<\/li>\n
    17. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrcrl} \\dfrac{1}{\\text{full}}&-&\\dfrac{1}{\\text{empty}}&=&\\dfrac{1}{2 T} \\\\ \\\\ \\dfrac{1}{10\\text{ h}}&-&\\dfrac{1}{15\\text{ h}}&=&\\dfrac{1}{2 T} \\\\ \\\\ \\dfrac{3}{30\\text{ h}}&-&\\dfrac{2}{30\\text{ h}}&=&\\dfrac{1}{2 T} \\\\ \\\\ &&\\dfrac{1}{30\\text{ h}}&=&\\dfrac{1}{2 T} \\\\ \\\\ &&2T&=&30\\text{ h} \\\\ \\\\ &&T&=&\\dfrac{30\\text{ h}}{2} \\\\ \\\\ &&T&=&15\\text{ h} \\end{array}[\/latex]<\/li>\n
    18. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrcrl} \\dfrac{1}{\\text{full}}&-&\\dfrac{1}{\\text{empty}}&=&\\dfrac{3}{4T} \\\\ \\\\ \\dfrac{1}{6\\text{ min}}&-&\\dfrac{1}{8\\text{ min}}&=&\\dfrac{3}{4T} \\\\ \\\\ \\dfrac{4}{24\\text{ min}}&-&\\dfrac{3}{24\\text{ min}}&=&\\dfrac{3}{4T} \\\\ \\\\ &&\\therefore \\dfrac{1}{24\\text{ min}}&=&\\dfrac{3}{4T} \\\\ \\\\ &&T&=&\\dfrac{3}{4}(24\\text{ min}) \\\\ \\\\ &&T&=&18\\text{ min} \\end{array}[\/latex]<\/li>\n
    19. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrcrl} \\dfrac{1}{H}&+&\\dfrac{1}{C}&=&\\dfrac{1}{T} \\\\ \\\\ \\dfrac{1}{H}&+&\\dfrac{1}{3.5\\text{ min}}&=&\\dfrac{1}{2.1\\text{ min}} \\\\ \\\\ &&\\dfrac{1}{H}&=&\\dfrac{1}{2.1\\text{ min}}-\\dfrac{1}{3.5\\text{ min}} \\\\ \\\\ &&\\dfrac{1}{H}&=&\\dfrac{50}{105\\text{ min}}-\\dfrac{30}{105\\text{ min}} \\\\ \\\\ &&\\dfrac{1}{H}&=&\\dfrac{20}{105\\text{ min}} \\\\ \\\\ &&\\dfrac{1}{H}&=&\\dfrac{4}{21\\text{ min}} \\\\ \\\\ &&H&=&\\dfrac{21}{4}\\text{ min} \\\\ \\\\ &&H&=&5.25 \\text{ min} \\end{array}[\/latex]<\/li>\n
    20. [latex]\\phantom{a}[\/latex]
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