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小升初 第七讲(工程类问题)

小升初  第七讲(工程类问题)
小升初  第七讲(工程类问题)

辅导讲义

教学内容

一、同步知识梳理

在日常生活中,做某一件事,制造某种产品,完成某项任务,完成某项工程等等,都要涉及到工作量、工作效率、工作时间这三个量,它们之间的基本数量关系是

工作总量=工作效率×时间

在小学数学中,探讨这三个数量之间关系的应用题,我们都叫做“工程问题”。

二、同步题型分析

【题型1】一般问题

例1、一件工作,由甲单独完成,需要10天,由乙单独完成需要15天。如果甲、乙合作完成,需要几天完成?

例2、一个水池有甲、乙两个水管,单开甲管2小时可以把水池注满,单开乙管3小时可以把满池水放完。如果同时打开甲、乙两管,几小时后水池可以注满?

例3、小红单独打印一份文件,需要5小时。要打印这份文件的2/3需要多少小时?

例4、甲、乙两人合作加工一批零件,需要25天完成。先由甲单独加工10天,再由乙单独加工30天,这时共加工了这批零件的3/4。乙每天能加工这批零件的几分之几?

【题型2】两个人的问题

例1、一件工作,甲做9天可以完成,乙做6天可以完成.现在甲先做了3天,余下的工作由乙继续

完成.乙需要做几天可以完成全部工作?

例2、一件工作,甲、乙两人合作30天可以完成,共同做了6天后,甲离开了,由乙继续做了40天才完成.如果这件工作由甲或乙单独完成各需要多少天?

例3、某工程先由甲独做63天,再由乙单独做28天即可完成;如果由甲、乙两人合作,需48天完成.现在甲先单独做42天,然后再由乙来单独完成,那么乙还需要做多少天?

例4、一件工程,甲队单独做10天完成,乙队单独做30天完成.现在两队合作,其间甲队休息了2天,乙队休息了8天(不存在两队同一天休息).问开始到完工共用了多少天时间?

例5、一项工程,甲队单独做20天完成,乙队单独做30天完成.现在他们两队一起做,其间甲队休息了3天,乙队休息了若干天.从开始到完成共用了16天.问乙队休息了多少天?

【题型3】多人的工程问题

例1、一件工作,甲、乙两人合作36天完成,乙、丙两人合作45天完成,甲、丙两人合作要60天完成.问甲一人独做需要多少天完成?

例2、一件工作,甲独做要12天,乙独做要18天,丙独做要24天.这件工作由甲先做了若干天,然后由乙接着做,乙做的天数是甲做的天数的3倍,再由丙接着做,丙做的天数是乙做的天数的2倍,终于做完了这件工作.问总共用了多少天?

例3、一项工程,甲、乙、丙三人合作需要13天完成.如果丙休息2天,乙就要多做4天,或者由甲、乙两人合作1天.问这项工程由甲独做需要多少天?

例4、某项工作,甲组3人8天能完成工作,乙组4人7天也能完成工作.问甲组2人和乙组7人合作多少时间能完成这项工作?

例5、制作一批零件,甲车间要10天完成,如果甲车间与乙车间一起做只要6天就能完成.乙车间与丙车间一起做,需要8天才能完成.现在三个车间一起做,完成后发现甲车间比乙车间多制作零件2400个.问丙车间制作了多少个零件?

【题型4】水管问题

例1、甲、乙两管同时打开,9分钟能注满水池.现在,先打开甲管,10分钟后打开乙管,经过3分钟就注满了水池.已知甲管比乙管每分钟多注入0.6立方米水,这个水池的容积是多少立方米?

例2、一个蓄水池,每分钟流入4立方米水.如果打开5个水龙头,2小时半就把水池水放空,如果

打开8个水龙头,1小时半就把水池水放空.现在打开13个水龙头,问要多少时间才能把水放空?

例3、一个水池,地下水从四壁渗入池中,每小时渗入水量是固定的.打开A 管,8小时可将满池水排空,打开C 管,12小时可将满池水排空.如果打开A ,B 两管,4小时可将水排空.问打开B ,C 两管,要几小时才能将满池水排空?

三、课堂达标检测

1、有两支成分不同且长度相等的蜡烛,其中一支3小时可燃烧完,另一支4小时燃烧完,现在要求到下午四点钟时,其中一支蜡烛的剩余部分恰是另一支剩余部分的两倍,问应何时点燃这两支蜡烛?

2、甲、乙、丙三人合作完成一项工程,共得报酬1800元,三人完成这项工程的情况是:甲、乙合作8天完成这项工程的3

1;接着乙、丙又合作2天,完成余下的41;以后3人合作5天完成了这项工程,按劳付酬,每人各应得报酬多少元?

3、一项工程甲、乙合作完成了全工程的

10

7,剩下的由甲单独完成,甲一共做了21天,这项工程由甲单独做需30天,如果由乙单独做,需多少天?

学法升华

一、知识收获

工程问题最基本的公式是什么?

二、方法总结

工程问题和行程问题的异同点是什么?

三、技巧提炼

你会用方程解工程问题吗?

课后作业

1、王师傅加工一批零件,计划在六月份每天都能超额完成当天任务的15%,后来因机器维修,最后的5天每天只完成当天任务的八成,就这样,六月份共超额加工660个零件,王师傅原来的任务是每天加工多少个零件?

2、甲、乙合作完成一项工作,由于配合得好,甲的工作效率比独做时提高了十分之一,乙的工作效率比独做时提高了五分之一,甲、乙两人合作4小时,完成全部工作的五分之二。第二天乙又独做了4小时,还剩下这件工作的三十分之十三没完成。这项工作甲独做需要几个小时才能完成?

3、一项工程A、B两人合作6天可以完成。如果A先做3天,B再接着做7天,可以完成,B单独完成这项工程需要多少天?

4、某工程,由甲乙两队承包,2.4天可以完成,需支付1800元,由乙丙两队承包,3又3/4天可以完成,需支付1500元,由甲丙两队承包,2又6/7天可以完成,需支付1600元,在保证一星期内完成的前提下,选择哪个队单独承包费用最少?

5、甲、乙二人同时开始加工一批零件,加单独做要20小时,乙单独做30小时。现在两人合作,工作了15小时后完成任务。已知甲休息了4小时,则乙休息了几小时?

最新小升初英语阅读理解及答案

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hide hid 隐藏 是(表示存在、状态等) is was 保持;使保持某种状态 keep kept 知道;了解 know knew 离去;出发 leave left 允许;让 let let 失去;丧失 lose lost 使;促使;迫使;做;制作make made 可能;可以 may might 表示……的意思;作……的解释mean meant 遇见;相逢 meet met 放;摆;装 put put read read /e/ 读;阅读 骑 ride rode (铃)响 ring rang rise rose 上升 跑;奔跑 run ran 说;讲 say said see saw 看见 发送;寄;派;遣 send sent set set 放, 置 出示;给 ... 看 show showed 关上(门、盖、窗户等) shut shut 唱;唱歌 sing sang sit sat 坐 睡;睡觉 sleep slept 说;说话 speak spoke swim swam 游泳

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四、左右两边都有X 的方程 根据等式的性质,把方程一边的X 消掉,然后根据上面讲过的步骤进行 移项:将方程中的某些项改变符号后,从方程的一边移到另一边的变形叫做移项。 6759x x +=+ 5563x x -=- 214632 x x +=+ 5986x x +=- 33624 x x -= 45-2x=3x+30 21x-32=31+0.25x 1381020x x +=+ 4.5 2.650% 3.4x x -=+ 6.3 2.530.8x x -=+ 3.32 5.651x x x +-=+ 去括号 ()x x +=+453 113 ()()12123--=+-x x x ()()15225-=+x x ()()x x x 31121+=--+

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小升初所有不规则动词的过去式 [ɑ:]are是(第二人称)[w?:]were [?m]am是(第一人称)[w?z]was [iz]is是(第三人称)[w?z]was [bε?]bear出生[b?:]bore [bi'k?m]become成为[bi'keim]became [bi'gin]begin开始[bi'g?n]began [bl?u]blow殴打[blu:]blew [breik]break打断[br?uk]broke [bri?]bring带来[br?:t] brought [bild]build建造[bilt]built [b?:n]burn烧伤[b?:nt] burnt、burned [bai]buy购买[b?:t]bought [k?n]can可以[kud]could [k?t∫]catch捕捉[k?:t]caught [t∫u:z]choose选择[t??uz]chose [k?m]come到达[keim]came [k?st]cost花费[k?st]cost [du:]do做[did]did [dr?:]draw绘制[dru:]drew [dri:m]dream做梦[dremt] dreamt、dreamed [dr??k]drink喝[dr??k]drank [draiv]drive驾驶[dr??k]drank [i:t]eat吃[eit]ate [f?:l]fall掉落[fel]fell [fi:d]feed喂养[fed]fed [fi:l]feel感到[felt]felt [fait]fight打架[f?:t]fought [faind]find查找[faund]found [fit]fit适合['fitid]fitted [flai]fly飞翔[flu:]flew [f?'ɡet]forge t忘记[f?'g?t]forgot [ɡet]get获得[g?t]got [ɡiv]give授予[geiv]gave [ɡ?u]go离去[went]went [ɡr?u]grow生长[gru:]grew [h??]hang闲逛[h??] hung hanged [h?v]have有[h?d]had [hi?]hear听到[h?:d]heard [h?uld]hold持有[held]held [h?:t]hurt伤害[h?:t]hurt [ki:p]keep保持[kept]kept [n?u]know知道[nju:]knew [l?:n]learn学习[l?:nt] learnt learned

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2 575 7557 5=-=-=-+=+x x x x 解: 3 3 9934 534 54435 43=÷==+=+=+-=-x x x x x x 解: 如果把画框的部分省略,我们把一个数从等号的左边移到右边的过程,叫做移项, 注意把一个数从方程的左边移到右边时,原来是加的变成减,原来是减的变成加号。 练习 552=-x 1264=-x 73 1 65%25?=-x 5364+=-x x 2.典型的例子及解方程的一般步骤; 2 6 31 737 313171 37==-==++==-x x x x x x 解: 5.0147714147147=÷====÷x x x x x 解: 11 34656453) 32(2532 )32()53(=-=+-=+-=+=-÷+x x x x x x x x x 解: 练习 7517=-x 7321=÷x 20484 3 3=-?x 3)13()511(=-÷-x x 3.解方程的一般步骤:

新版小学小升初英语阅读理解及答案【解析】 (15)

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