thrift of excellent traditional and style lack deep of understanding, one-sided think in now of good situation Xia, economic smooth more fast development, and reform made major progress, and people living significantly improve, and social the career made new progress, no necessary always hard has, no awareness to China also has many poverty area, and also has many poverty population of exists, more living improve has, more need keep hard of style. Three is not strictly honest. Total thought units is a water sector, clean self-discipline away from himself too far, no real processing good living of improve and hard, and thrift excellent traditional of relationship, no effective do comply with Constitution and party of regulations must from I do up, no right mercy good bitter Le, and wealth of relationship, no right awareness to in comply with Constitution and party of regulations aspects everyone has accountability. Four, future direction and improvement measures 1, belief and faith, strengthen party spirit. One is to firmly establish the noble ideals of struggle for the ideals of communism, communist struggle for life, ready to sacrifice everything for the party and the people. Second is to continuously improve the quality and standard of political, conscientiously study Deng Xiaoping theory and \ Third, strengthening the party spirit and the world transformation, perseverance of the party Constitution, relive Party vows to establish correct world Outlook, Outlook on life and the world, practically embodies ideals and beliefs into action, combine lofty ideals and practical activities, transforming the objective world, actively participate in the great practice of building socialism with Chinese characteristics. 2, keep the purpose in concept, changing the style of work. First, keep in mind that the purpose of serving, adhere to assuming power for the people, keep in mind the people and care about people, and the joys and sorrows of the masses, ... According to city discipline, and municipal organization Department requirements, today we held \一元一次方程应用题分类讲评
一元一次方程应用题是初一数学学习的重点，也是一个难点。主要困难体现在两个方面：一是难以从实际问题中找出相等关系，列出相应的方程；二是对数量关系稍复杂的方程，常常理不清楚基本量，也不知道如何用含未知数的式子来表示出这些基本量的相等关系，导致解题时无从下手。
事实上，方程就是一个含未知数的等式。列方程解应用题，就是要将实际问题中的一些数量关系用这种含有未知数的等式的形式表示出来。而在这种等式中的每个式子又都有自身的实际意义，它们分别表示题设中某一相应过程的数量大小或数量关系。由此，解方程应用题的关键就是要“抓住基本量，找出相等关系”。
下面就一元一次方程中常见的几类应用题作逐一讲评，供同学们学习时参考。
1.行程问题
行程问题中有三个基本量：路程、时间、速度。关系式为：①路程=速度×时间；②速度=
；③时间=
。
project work, cadres, cadres selection and other aspects of a total of 19, further defined the direction of rectification, enhancing the pertinence and effectiveness of democratic life. Good for this meeting, we requested the Standing Committee of the municipal party Committee, municipal Secretary General Tang Wenjin, the City Commission for discipline inspection Standing Committee Yang Xu, Jiang Jixue, Deputy Director of the personnel office, and other leading comrades present guidance allows us to warm applause for their welcome and thanks! Below, I first District Committee member of the 20XX team annual democratic meeting implementation of the corrective measures, as well as member of the team and of my own report guidelines for the implementation of the independent Commission against corruption statement invited leaders and comrades criticism. First, annual party on the 20XX team, Member of democratic life action plan implementation year 20XX, district democratic meeting a member of the team on \ Year of 20XX, we find out the problems mentioned above, based on actual Shunqing construction and development, conscientiously sum up improvements, achieving significant development results and effectiveness of their work. (A) highlight the project handle, maintain high growth of investment. Adhere to the strategy as a Foundation, carrying out projects to promote increased stamina important. One is to increase the intensity of projects towards. Actively seek national and provincial policy support, superior special transfer payments, a variety of additional income will top 700 million Yuan, a number of key infrastructure projects, livelihood projects, industrial projects into the cage. Second, increasing the project attracts. This year a total of 23 signed a major project, of which 14 billion project, China Metallurgical group, vanke group, Guangdong hengda group, Taiwan Ruentex group, on the RI group, Shenzhen Kaisa, jifeng agricultural machinery, Mercedes-Benz, Audi 4S store and other large enterprises and projects have settled in Shunqing. Third, strengthen project construction. Annual implementation focus project 39 a, fixed assets investment total will breakthrough 12 billion yuan, created district yilai history high, South door dam, and five in shop old city transformation, and Ying China industrial concentrated district construction, and city main road construction, and Northeast steam Trade Center, and modern farmers industry Park, and vocational education city, and low rental, and also room construction, and features blocks build, and farmers market transformation, and \engineering speed up implementation, effectiveness obviously. Expected to be achieved this year, area-wide GDP 17 billionthrift of excellent traditional and style lack deep of understanding, one-sided think in now of good situation Xia, economic smooth more fast development, and reform made major progress, and people living significantly improve, and social the career made new progress, no necessary always hard has, no awareness to China also has many poverty area, and also has many poverty population of exists, more living improve has, more need keep hard of style. Three is not strictly honest. Total thought units is a water sector, clean self-discipline away from himself too far, no real processing good living of improve and hard, and thrift excellent traditional of relationship, no effective do comply with Constitution and party of regulations must from I do up, no right mercy good bitter Le, and wealth of relationship, no right awareness to in comply with Constitution and party of regulations aspects everyone has accountability. Four, future direction and improvement measures 1, belief and faith, strengthen party spirit. One is to firmly establish the noble ideals of struggle for the ideals of communism, communist struggle for life, ready to sacrifice everything for the party and the people. Second is to continuously improve the quality and standard of political, conscientiously study Deng Xiaoping theory and \ Third, strengthening the party spirit and the world transformation, perseverance of the party Constitution, relive Party vows to establish correct world Outlook, Outlook on life and the world, practically embodies ideals and beliefs into action, combine lofty ideals and practical activities, transforming the objective world, actively participate in the great practice of building socialism with Chinese characteristics. 2, keep the purpose in concept, changing the style of work. First, keep in mind that the purpose of serving, adhere to assuming power for the people, keep in mind the people and care about people, and the joys and sorrows of the masses, ... According to city discipline, and municipal organization Department requirements, today we held \
可寻找的相等关系有：路程关系、时间关系、速度关系。在不同的问题中，相等关系是灵活多变的。如相遇问题中多以路程作相等关系，而对有先后顺序的问题却通常以时间作相等关系，在航行问题中很多时候还用速度作相等关系。
航行问题是行程问题中的一种特殊情况，其速度在不同的条件下会发生变化：①顺水（风）速度=静水（无风）速度+水流速度（风速）；②逆水（风）速度=静水（无风）速度－水流速度（风速）。由此可得到航行问题中一个重要等量关系：顺水（风）速度－水流速度（风速）＝逆水（风）速度+水流速度（风速）＝静水（无风）速度。
例１．某队伍450米长，以每分钟90米速度前进，某人从排尾到排头取东西后，立即返回排尾，速度为3米/秒。问往返共需多少时间？
讲评：这一问题实际上分为两个过程：①从排尾到排头的过程是一个追及过程，相当于最后一个人追上最前面的人；②从排头回到排尾的过程则是一个相遇过程，相当于从排头走到与排尾的人相遇。
project work, cadres, cadres selection and other aspects of a total of 19, further defined the direction of rectification, enhancing the pertinence and effectiveness of democratic life. Good for this meeting, we requested the Standing Committee of the municipal party Committee, municipal Secretary General Tang Wenjin, the City Commission for discipline inspection Standing Committee Yang Xu, Jiang Jixue, Deputy Director of the personnel office, and other leading comrades present guidance allows us to warm applause for their welcome and thanks! Below, I first District Committee member of the 20XX team annual democratic meeting implementation of the corrective measures, as well as member of the team and of my own report guidelines for the implementation of the independent Commission against corruption statement invited leaders and comrades criticism. First, annual party on the 20XX team, Member of democratic life action plan implementation year 20XX, district democratic meeting a member of the team on \ Year of 20XX, we find out the problems mentioned above, based on actual Shunqing construction and development, conscientiously sum up improvements, achieving significant development results and effectiveness of their work. (A) highlight the project handle, maintain high growth of investment. Adhere to the strategy as a Foundation, carrying out projects to promote increased stamina important. One is to increase the intensity of projects towards. Actively seek national and provincial policy support, superior special transfer payments, a variety of additional income will top 700 million Yuan, a number of key infrastructure projects, livelihood projects, industrial projects into the cage. Second, increasing the project attracts. This year a total of 23 signed a major project, of which 14 billion project, China Metallurgical group, vanke group, Guangdong hengda group, Taiwan Ruentex group, on the RI group, Shenzhen Kaisa, jifeng agricultural machinery, Mercedes-Benz, Audi 4S store and other large enterprises and projects have settled in Shunqing. Third, strengthen project construction. Annual implementation focus project 39 a, fixed assets investment total will breakthrough 12 billion yuan, created district yilai history high, South door dam, and five in shop old city transformation, and Ying China industrial concentrated district construction, and city main road construction, and Northeast steam Trade Center, and modern farmers industry Park, and vocational education city, and low rental, and also room construction, and features blocks build, and farmers market transformation, and \engineering speed up implementation, effectiveness obviously. Expected to be achieved this year, area-wide GDP 17 billionthrift of excellent traditional and style lack deep of understanding, one-sided think in now of good situation Xia, economic smooth more fast development, and reform made major progress, and people living significantly improve, and social the career made new progress, no necessary always hard has, no awareness to China also has many poverty area, and also has many poverty population of exists, more living improve has, more need keep hard of style. Three is not strictly honest. Total thought units is a water sector, clean self-discipline away from himself too far, no real processing good living of improve and hard, and thrift excellent traditional of relationship, no effective do comply with Constitution and party of regulations must from I do up, no right mercy good bitter Le, and wealth of relationship, no right awareness to in comply with Constitution and party of regulations aspects everyone has accountability. Four, future direction and improvement measures 1, belief and faith, strengthen party spirit. One is to firmly establish the noble ideals of struggle for the ideals of communism, communist struggle for life, ready to sacrifice everything for the party and the people. Second is to continuously improve the quality and standard of political, conscientiously study Deng Xiaoping theory and \ Third, strengthening the party spirit and the world transformation, perseverance of the party Constitution, relive Party vows to establish correct world Outlook, Outlook on life and the world, practically embodies ideals and beliefs into action, combine lofty ideals and practical activities, transforming the objective world, actively participate in the great practice of building socialism with Chinese characteristics. 2, keep the purpose in concept, changing the style of work. First, keep in mind that the purpose of serving, adhere to assuming power for the people, keep in mind the people and care about people, and the joys and sorrows of the masses, ... According to city discipline, and municipal organization Department requirements, today we held \
在追及过程中，设追及的时间为x秒，队伍行进（即排头）速度为90米/分=1.5米/秒，则排头行驶的路程为1.5x米；追及者的速度为3米/秒，则追及者行驶的路程为3x米。由追及问题中的相等关系“追赶者的路程－被追者的路程=原来相隔的路程”，有：
3x－1.5x=450 ∴x=300
在相遇过程中，设相遇的时间为y秒，队伍和返回的人速度未变，故排尾人行驶的路程为1.5y米，返回者行驶的路程为3y米，由相遇问题中的相等关系“甲行驶的路程+乙行驶的路程=总路程”有： 3y+1.5y=450 ∴y=100
故往返共需的时间为 x+y=300+100=400（秒）
例2 汽车从A地到B地，若每小时行驶40km，就要晚到半小时：若每小时行驶45km，就可以早到半小时。求A、B 两地的距离。
讲评：先出发后到、后出发先到、快者要早到慢者要晚到等问题，我们通常都称其为“先后问题”。在这类问题
project work, cadres, cadres selection and other aspects of a total of 19, further defined the direction of rectification, enhancing the pertinence and effectiveness of democratic life. Good for this meeting, we requested the Standing Committee of the municipal party Committee, municipal Secretary General Tang Wenjin, the City Commission for discipline inspection Standing Committee Yang Xu, Jiang Jixue, Deputy Director of the personnel office, and other leading comrades present guidance allows us to warm applause for their welcome and thanks! Below, I first District Committee member of the 20XX team annual democratic meeting implementation of the corrective measures, as well as member of the team and of my own report guidelines for the implementation of the independent Commission against corruption statement invited leaders and comrades criticism. First, annual party on the 20XX team, Member of democratic life action plan implementation year 20XX, district democratic meeting a member of the team on \ Year of 20XX, we find out the problems mentioned above, based on actual Shunqing construction and development, conscientiously sum up improvements, achieving significant development results and effectiveness of their work. (A) highlight the project handle, maintain high growth of investment. Adhere to the strategy as a Foundation, carrying out projects to promote increased stamina important. One is to increase the intensity of projects towards. Actively seek national and provincial policy support, superior special transfer payments, a variety of additional income will top 700 million Yuan, a number of key infrastructure projects, livelihood projects, industrial projects into the cage. Second, increasing the project attracts. This year a total of 23 signed a major project, of which 14 billion project, China Metallurgical group, vanke group, Guangdong hengda group, Taiwan Ruentex group, on the RI group, Shenzhen Kaisa, jifeng agricultural machinery, Mercedes-Benz, Audi 4S store and other large enterprises and projects have settled in Shunqing. Third, strengthen project construction. Annual implementation focus project 39 a, fixed assets investment total will breakthrough 12 billion yuan, created district yilai history high, South door dam, and five in shop old city transformation, and Ying China industrial concentrated district construction, and city main road construction, and Northeast steam Trade Center, and modern farmers industry Park, and vocational education city, and low rental, and also room construction, and features blocks build, and farmers market transformation, and \engineering speed up implementation, effectiveness obviously. Expected to be achieved this year, area-wide GDP 17 billionthrift of excellent traditional and style lack deep of understanding, one-sided think in now of good situation Xia, economic smooth more fast development, and reform made major progress, and people living significantly improve, and social the career made new progress, no necessary always hard has, no awareness to China also has many poverty area, and also has many poverty population of exists, more living improve has, more need keep hard of style. Three is not strictly honest. Total thought units is a water sector, clean self-discipline away from himself too far, no real processing good living of improve and hard, and thrift excellent traditional of relationship, no effective do comply with Constitution and party of regulations must from I do up, no right mercy good bitter Le, and wealth of relationship, no right awareness to in comply with Constitution and party of regulations aspects everyone has accountability. Four, future direction and improvement measures 1, belief and faith, strengthen party spirit. One is to firmly establish the noble ideals of struggle for the ideals of communism, communist struggle for life, ready to sacrifice everything for the party and the people. Second is to continuously improve the quality and standard of political, conscientiously study Deng Xiaoping theory and \ Third, strengthening the party spirit and the world transformation, perseverance of the party Constitution, relive Party vows to establish correct world Outlook, Outlook on life and the world, practically embodies ideals and beliefs into action, combine lofty ideals and practical activities, transforming the objective world, actively participate in the great practice of building socialism with Chinese characteristics. 2, keep the purpose in concept, changing the style of work. First, keep in mind that the purpose of serving, adhere to assuming power for the people, keep in mind the people and care about people, and the joys and sorrows of the masses, ... According to city discipline, and municipal organization Department requirements, today we held \中主要考虑时间量，考察两者的时间关系，从相隔的时间上找出相等关系。本题中，设A、B两地的路程为x km，速度为40 km/小时，则时间为则时间为
例3 一艘轮船在甲、乙两地之间行驶，顺流航行需6小时，逆流航行需8小时，已知水流速度每小时2 km。求
小时；速度为45 km/小时，
小时，又早到与晚到之间相隔1小时，故有
－ = 1 ∴ x = 360
甲、乙两地之间的距离。
讲评：设甲、乙两地之间的距离为x km，则顺流速度为km/小时，逆流速度为km/小时，由航行问题中的重要等量关系有：
－２= +2 ∴ x = 96
project work, cadres, cadres selection and other aspects of a total of 19, further defined the direction of rectification, enhancing the pertinence and effectiveness of democratic life. Good for this meeting, we requested the Standing Committee of the municipal party Committee, municipal Secretary General Tang Wenjin, the City Commission for discipline inspection Standing Committee Yang Xu, Jiang Jixue, Deputy Director of the personnel office, and other leading comrades present guidance allows us to warm applause for their welcome and thanks! Below, I first District Committee member of the 20XX team annual democratic meeting implementation of the corrective measures, as well as member of the team and of my own report guidelines for the implementation of the independent Commission against corruption statement invited leaders and comrades criticism. First, annual party on the 20XX team, Member of democratic life action plan implementation year 20XX, district democratic meeting a member of the team on \ Year of 20XX, we find out the problems mentioned above, based on actual Shunqing construction and development, conscientiously sum up improvements, achieving significant development results and effectiveness of their work. (A) highlight the project handle, maintain high growth of investment. Adhere to the strategy as a Foundation, carrying out projects to promote increased stamina important. One is to increase the intensity of projects towards. Actively seek national and provincial policy support, superior special transfer payments, a variety of additional income will top 700 million Yuan, a number of key infrastructure projects, livelihood projects, industrial projects into the cage. Second, increasing the project attracts. This year a total of 23 signed a major project, of which 14 billion project, China Metallurgical group, vanke group, Guangdong hengda group, Taiwan Ruentex group, on the RI group, Shenzhen Kaisa, jifeng agricultural machinery, Mercedes-Benz, Audi 4S store and other large enterprises and projects have settled in Shunqing. Third, strengthen project construction. Annual implementation focus project 39 a, fixed assets investment total will breakthrough 12 billion yuan, created district yilai history high, South door dam, and five in shop old city transformation, and Ying China industrial concentrated district construction, and city main road construction, and Northeast steam Trade Center, and modern farmers industry Park, and vocational education city, and low rental, and also room construction, and features blocks build, and farmers market transformation, and \engineering speed up implementation, effectiveness obviously. Expected to be achieved this year, area-wide GDP 17 billionthrift of excellent traditional and style lack deep of understanding, one-sided think in now of good situation Xia, economic smooth more fast development, and reform made major progress, and people living significantly improve, and social the career made new progress, no necessary always hard has, no awareness to China also has many poverty area, and also has many poverty population of exists, more living improve has, more need keep hard of style. Three is not strictly honest. Total thought units is a water sector, clean self-discipline away from himself too far, no real processing good living of improve and hard, and thrift excellent traditional of relationship, no effective do comply with Constitution and party of regulations must from I do up, no right mercy good bitter Le, and wealth of relationship, no right awareness to in comply with Constitution and party of regulations aspects everyone has accountability. Four, future direction and improvement measures 1, belief and faith, strengthen party spirit. One is to firmly establish the noble ideals of struggle for the ideals of communism, communist struggle for life, ready to sacrifice everything for the party and the people. Second is to continuously improve the quality and standard of political, conscientiously study Deng Xiaoping theory and \ Third, strengthening the party spirit and the world transformation, perseverance of the party Constitution, relive Party vows to establish correct world Outlook, Outlook on life and the world, practically embodies ideals and beliefs into action, combine lofty ideals and practical activities, transforming the objective world, actively participate in the great practice of building socialism with Chinese characteristics. 2, keep the purpose in concept, changing the style of work. First, keep in mind that the purpose of serving, adhere to assuming power for the people, keep in mind the people and care about people, and the joys and sorrows of the masses, ... According to city discipline, and municipal organization Department requirements, today we held \ 2.工程问题
工程问题的基本量有：工作量、工作效率、工作时间。关系式为：①工作量=工作效率×工作时间。②工作时间=
，③工作效率=
工程问题中，一般常将全部工作量看作整体1，如果完成全部工作的时间为t，则工作效率为。常见的相等关系有两种：①如果以工作量作相等关系，部分工作量之和=总工作量。②如果以时间作相等关系，完成同一工作的时间差=多用的时间。
在工程问题中，还要注意有些问题中工作量给出了明确的数量，这时不能看作整体1，此时工作效率也即工作速度。
。
project work, cadres, cadres selection and other aspects of a total of 19, further defined the direction of rectification, enhancing the pertinence and effectiveness of democratic life. Good for this meeting, we requested the Standing Committee of the municipal party Committee, municipal Secretary General Tang Wenjin, the City Commission for discipline inspection Standing Committee Yang Xu, Jiang Jixue, Deputy Director of the personnel office, and other leading comrades present guidance allows us to warm applause for their welcome and thanks! Below, I first District Committee member of the 20XX team annual democratic meeting implementation of the corrective measures, as well as member of the team and of my own report guidelines for the implementation of the independent Commission against corruption statement invited leaders and comrades criticism. First, annual party on the 20XX team, Member of democratic life action plan implementation year 20XX, district democratic meeting a member of the team on \ Year of 20XX, we find out the problems mentioned above, based on actual Shunqing construction and development, conscientiously sum up improvements, achieving significant development results and effectiveness of their work. (A) highlight the project handle, maintain high growth of investment. Adhere to the strategy as a Foundation, carrying out projects to promote increased stamina important. One is to increase the intensity of projects towards. Actively seek national and provincial policy support, superior special transfer payments, a variety of additional income will top 700 million Yuan, a number of key infrastructure projects, livelihood projects, industrial projects into the cage. Second, increasing the project attracts. This year a total of 23 signed a major project, of which 14 billion project, China Metallurgical group, vanke group, Guangdong hengda group, Taiwan Ruentex group, on the RI group, Shenzhen Kaisa, jifeng agricultural machinery, Mercedes-Benz, Audi 4S store and other large enterprises and projects have settled in Shunqing. Third, strengthen project construction. Annual implementation focus project 39 a, fixed assets investment total will breakthrough 12 billion yuan, created district yilai history high, South door dam, and five in shop old city transformation, and Ying China industrial concentrated district construction, and city main road construction, and Northeast steam Trade Center, and modern farmers industry Park, and vocational education city, and low rental, and also room construction, and features blocks build, and farmers market transformation, and \engineering speed up implementation, effectiveness obviously. Expected to be achieved this year, area-wide GDP 17 billion
一元一次方程应用题
