全俄中学生数学奥林匹克

wjsw

<p align="center" style="TEXT-ALIGN: center;"><b style="mso-bidi-font-weight: normal;"><span style="FONT-SIZE: 16pt; FONT-FAMILY: 黑体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman';">全俄中学生数学奥林匹克</span></b><b style="mso-bidi-font-weight: normal;"><span lang="EN-US" style="FONT-SIZE: 16pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-fareast-font-family: 黑体;"><p></p></span></b></p><p align="center" style="TEXT-ALIGN: center;"><span style="FONT-SIZE: 14pt; mso-ascii-font-family: &quot;Times New Roman&quot;;"><font face="宋体">（第</font></span><span lang="EN-US" style="FONT-SIZE: 14pt; FONT-FAMILY: &quot;Times New Roman&quot;;">25</span><font face="宋体"><span style="FONT-SIZE: 14pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">届第</span><span lang="EN-US" style="FONT-SIZE: 14pt;">Ⅳ</span><span style="FONT-SIZE: 14pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">阶段</span></font><span style="FONT-SIZE: 14pt; FONT-FAMILY: 黑体; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-ascii-font-family: &quot;Times New Roman&quot;;">八年级试题）</span><span lang="EN-US" style="FONT-SIZE: 14pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-fareast-font-family: 黑体;"><p></p></span></p><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">1</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">、父亲带着两个儿子向离城</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">33</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">公里的祖母家出发，父亲有一辆摩托车，速度为</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">25</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">公里／小时．如果再载了另一个人，则速度为</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">20</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">公里／小时，（摩托车不允许带两个人，即每车至多载两人。）每个儿子如果步行，速度为</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">5</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">公里／小时。证明：这</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">3</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">个人可在</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">3</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">小时内同时到达祖母家。</span>

wjsw

<p>换个心情，练练脑筋</p>

wjsw

<p><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;;"><span style="mso-spacerun: yes;">&nbsp; </span></span><b style="mso-bidi-font-weight: normal;"><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">证</span></b><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">：设第二个儿子先步行，父亲载着第一个儿子乘摩托车走了</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;;">x</span><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">公里，这里用了x/20</span><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">小时，并且他们超过第二个儿子x/20(20-5)=3x/4</span><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">公里）。这时，父亲让第一个儿子步行，自己返回去接第二个儿子。到遇到第二个儿子时，用了3x/4除以(20+5)=1x/40(</span><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">小时）。第二个儿子遇到父亲时，步行走了(x/20+x/40)*5=3x/8(</span><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">公里），这时离祖母家还有(33-3x/8)(</span><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">公里）。如果父亲载第二个儿子的路程与载第一个儿子的路程相同，那么x=33-3x/8</span><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">，所以</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;;">x=24</span><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">（公里）。这样，在路上共计用的时间为x/20+x/40+x/20=1/8*24=3</span><span style="FONT-SIZE: 10.5pt; mso-ascii-font-family: &quot;Times New Roman&quot;;">（小时.</span></p>

英雄无悔

我算了下可以在3小时以内