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1、第 1 页 共 13 页工程问题汇编工程问题是小学分数应用题中的一个重点，也是一个难点。下面列举有关练习中常见的几种题型，分别进行思路分析，并加以简要的评点，旨在使同学们掌握“工程问题”的解题规律和解题技巧。工程问题是研究工作效率、工作时间和工作总量之间相互关系的一种应用题。我们通常所说的：“工程问题”，一般是把工作总量作为单位“”，因此工作效率就是工作时间的倒数。它们的基本关系式是：工作总量 工作效率工作时间。一、基本工程问题例 1：甲、乙两队开挖一条水渠。甲队单独挖要 8 天完成，乙队单独挖要 12天完成。现在两队同时挖了几天后，乙队调走，余下的甲队在3 天内完成。乙队挖了多少天？例 2：
2、加工一批零件，甲单独做20 天可以完工，乙单独做30 天可以完工。现两队合作来完成这个任务，合作中甲休息了2.5 天，乙休息了若干天，这样共 14 天完工。乙休息了几天？例 3：一池水，甲、乙两管同时开，5 小时灌满，乙、丙两管同时开，4 小时灌满。现在先开乙管6 小时，还需甲、丙两管同时开2 小时才能灌满。乙单独开几小时可以灌满？例 4：某工程，甲、乙合作1 天可以完成全工程的245。如果这项工程由甲队单独做 2 天，再由乙队单独做 3 天，能完成全工程的2413。甲、乙两队单独完成这项工程各需要几天？例 5：一项工程，甲先单独做2天，然后与乙合做7 天，这样才能完成全工程的一半。已知甲、乙
3、工效的比是2:3。如果这项工程由乙单独做，需要多少天才能完成？例题详解：例 1 解：可以理解为甲队先做3 天后两队合挖的。第 2 页 共 13 页121813811=3（天）例 2 解：分析：共 14 天完工，说明甲做（142.5）天，其余是乙做的，用14天减去乙做的天数就是乙休息的天数。14301205.2141=141（天）例 3 解：分析：把乙先开做6 小时看作与甲做 2 小时，与丙做 2 小时，还有 2小时，现在可理解为甲乙同开2 小时，乙丙同开 2 小时，剩下的是乙 2 小时放的。12241511=20（小时）例 4 解：分析：可以理解为两队合作2 天，余下的是乙1 天做的，乙的工效
4、8122452413，甲：812451=12（天）例 5 解：分析：乙的工效是甲工效的32=1.5 倍，设甲的工效为 x，乙的工效为 1.5x，（2+7）x+1.5x7=21，解之得：x=391，乙工效 11.5x=26（天）基本练习（附参考答案）：1、修一条公路，甲队独修15 天完工，乙队独修 12 天完工。两队合修4 天后，乙队调走，剩下的路由甲队继续修完。甲队一共修了多少天？2、一项工程，甲单独做20 天完成，乙单独做30 天完成。甲、乙合做几天后，乙因事请假，甲继续做，从开工到完成任务共用了16 天。乙请假多少天？3、一条公路由甲、乙两个筑路队合修要12 天完成。现在由甲队修3 天后，
5、再由乙队修 1天，共修了这条公路的203。如果这条公路由甲队单独修，要多少天才能修完？4、两列火车同时从甲、乙两地同时相对开出。快车行完全程需要20 小时，慢车行完全程需要30 小时。开出后 15 小时两车相遇。已知快车中途停留4 小时，慢车停留了几小时？5、师徒两人共同加工一批零件，2 天加工了总数的31。这批零件如果全部由师傅单独加工，需 10 天完成。如果全部由徒弟加工，需要多少天才能完成？6、一项工程，甲、乙两队合作30 天完成。如果甲队单独做24 天后，乙队文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7
6、M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码
7、:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7
8、M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码
9、:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7
10、M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码
11、:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7
12、M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6第 3 页 共 13 页再加入合作，两队合作 12 天后，甲队因事离去，由乙队继续做了 15 天才完成。这项工程如果由甲队单独完成，需要多少天？7、一项工程，甲、乙两队合做每天能完成全工程的409。甲队独做 3 天，乙队独做 5 天后，可完成全工程的87。如果全工程由乙队单独做，多少天可以完成？8、甲、乙两队合作，20 天完成一项工程。如果两队合作8 天后，乙队再独做 4 天，还剩下这项工程的158。甲、乙两队独做各需几天完成？9、一项工程，甲、队独做10 天可以完成，乙队独做30
13、天可以完成。现在两队合作期间甲队休息了2 天，乙队休息了 8 天（两队不在同一天休息）。从开始到完工共用了多少天？10、一项工程，如甲队独做，可 6 天完成。甲 3 天的工作量，乙要 4 天完成。两队合做了 2天后，由乙队单独做，乙队还需做多少天才能完成？参考答案1、1511241=10（天）2、16301162011=10（天）3、113121203=120（天）4、153014152011=221（小时）5、1101231=15（天）6、分析：甲先做 24 天，乙最后做 15 天，可以理解为又合做15 天加先合做12 天，共合做 27 天。15242730111=90（天）7、可理解为两队
14、合做了3 天。353409871=10（天）文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5
15、D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 H
16、M3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5
17、D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 H
18、M3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5
19、D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 H
20、M3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6第 4 页 共 13 页8、乙的工效415882011=601乙需的天数：1601=60（天）甲乙需的天数：1601201=30（天）9、分析：可理解为甲多做6 天。30110161011+8=11（天）10、甲的工效61，乙的工效81463，81281611=331（天）二、工程问题的拓展题例 1：某工程先由甲单
21、独做63 天，再由乙队独做28 天即可以完成。如果甲、乙两人合作，需48 天完成，现在甲先独做42 天，然后再由乙单独完成，那么还需要多少天？例 2：一项工程，甲队单独做需30 天完成，乙队单独做需40 天完成。甲队先做若干天后，由乙队接着做，共用 36 天完成任务。甲、乙两队各做了多少天？例 3：搬运一个仓库的货物，甲需10 小时，乙需 12 小时，丙需 15 小时。有同样的仓库 A 和 B，甲在 A 仓库，乙在 B 仓库同时开始搬运货物，丙开始帮助甲搬运，中途又转向帮助乙搬运，最后同时搬完两个仓库的货物。丙帮助甲、乙各搬运了几小时？例 4：一项工程，乙队先独做4 天，继而甲、丙两队合做6
22、天，剩下的工程甲队又独做 9 天才全部完成。已知乙队完成的是甲队的31，丙队完成的是乙队的 2 倍。如果甲、乙、丙单独做，各需多少天？例 5：客车由甲站开往乙站需要8 小时，货车从乙站开往甲站需要12 小时。两车同时从两站相向开出，相遇时客车离乙站还有156 千米。两站相距多少千米？例题详解：例1分 析：可 以 理 解 为 两 队 合 做28天，甲 的 工 效：文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5
23、D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 H
24、M3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5
25、D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 H
26、M3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5
27、D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 H
28、M3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5
29、D6第 5 页 共 13 页8412863284811乙的 工 效：4811121841，还 要1 1 21428411=56（天）例 2 分析：设乙做 x 天，甲做（36x）天，xx36301401=1，解之得 x=24，甲做 36x=3624=12（天）例 3 分析：可以看作甲、乙、丙合作搬运 A、B 两仓，2151121101=8（小时），甲在 A 仓库运 8 小时，余下的是丙搬运的，乙在B 仓库搬运 8 小时，余下的是丙搬运的。丙运 A 仓库15181011=3（小时），丙运 B 仓库15181211=5（小时）例 4 分析：把乙做 4 天的工作量看作1 份，甲做（6+9）天的工作量看
30、作3 份，丙做 6 天的工作量看作2 份，把这项工程看作6 份。甲：11563=30（天），乙：1461=24（天），丙：1662=18（天）例 5 分析：156 除以货车相遇时所对应的分率：121811121156=390（千米）文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7
31、M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码
32、:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7
33、M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码
34、:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7
35、M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码
36、:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6第 6 页 共 13 页拓展练习（附参考答案）1、凿一山洞，甲队单独凿8 天完成，乙队单独凿12 天完成。现甲队单独凿了若干天后
37、留给乙队单独凿，两队先后共用 10 天完成，甲、乙两队各凿了多少天？2、甲、乙两台抽水机共同工作10 小时，可以把整池水抽完。如果甲台抽水机工作 4 小时，乙台抽水机工作6 小时，能抽完整池水的157。甲、乙两台抽水机单独工作，各需几小时才能将整池水抽完？3、一个水池甲、乙两个水管同时打开，5 小时可以灌满整个池水；如果甲管打开 8 小时后关闭，然后打开乙管，再工作3 小时也可以灌满全池水。如果甲管先工作 2 小时，然后关闭，乙管再工作几小时可以灌满全池水？4、一项工程，甲、乙合做6 天能完成65。单独做，甲完成31与乙完成21所需的时间相等。甲、乙单独做各需多少天？5、一项工作，甲、乙、丙三
38、人合做6 小时可以完成，如果甲工作6 小时，乙、丙合做 2 小时，可以完成这项工作的32。如果、乙合做 3 小时，丙做 6 小时，也可以完成这项工作的32。这项工作如果由甲、丙合做，需几小时完成？6、一池水，甲、乙两管同时开5 小时灌满；乙、丙管同时开4 小时灌满。现在先开乙管 6 小时还需甲、丙两管同时开2 小时才能灌满。乙单独开几小时可以灌满水池？7、一辆客车和一辆货车同时从甲、乙两站同时开出，经过 6 小时相遇。相遇后两车各以原速继续前进，客车又行了4 小时才到达乙地。货车还要行多少小时才能到达甲地？8、甲、乙两车同时从A、B 两地出发，相向而行。经过4 小时相遇后，甲车继续行驶了 3
39、小时到达 B 地，乙车每小时行 24 千米。A、B 两地相距多少千米？9、要用甲、乙两根水管灌满一个水池，开始只打开甲管，9 分钟后打开乙管，再过 4 分钟已灌入了31水池的水；再经过 10 分钟，灌入的水已占水池的32。这时关掉甲管只开乙管，从开始到灌满水池共用了多少钟？10、一个水池装了甲、乙两根进水管，在同样的时间内，乙管的进水量是甲管的 1.6 倍。为了灌满空着的水池，开始由甲管灌入51水池的水，然后打开乙管，剩下的由乙管单独灌满，总共用12 分 15 秒。甲管开了几小时？参考答案1、分析：理解为两队合做若干天后，剩下的由某队独做正好在10 天内完成。文档编码:CU1M9W9R5T4
40、HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H
41、5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4
42、HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H
43、5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4
44、HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H
45、5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4
46、HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6第 7 页 共 13 页544121811（天），甲、乙合做 4 天后，余下的54天合做的工作量是：1218154=61，工作量61不够甲做 2 天，由乙做61121=2（天）。甲共做 4 天，乙共做（4+2=6）天。2、分析：可理解为甲、乙合抽4 小时，用157减去合抽 4 小时后余下的是乙2小时抽的：乙工效464101157=301，甲工效151301101，甲要 15 小时，乙要 30
47、 小时。3、甲工效：252383511，乙工效：51252=25325322521=7（小时）4、3121=65，说明单独做甲完成31与乙完成21是甲、乙合做 6 天完成的，甲单独做：631=18（天），乙单独做：621=12（天）。5、分析：可理解为三人合做2 小时，用32减去合做 2 小时的，余下的是甲（62）小时做的。甲的工效：2626132=121，乙的工效：366332=181，1（121181）=751（小时）。6、分析：把乙开6 小时分 2 小时和甲开，又分2 小时和丙开，还剩2 小时是乙单独开的。文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文
48、档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I
49、2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文
50、档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I2F7M2K4 ZO1M8H1H5D6文档编码:CU1M9W9R5T4 HM3I