Школьники занимаются прополкой огорода, который находится на пришкольном участке. Работают они с разной скоростью, а некоторые из них, как показывает практика, даже мешают общей работе, просто закапывая сорняки или перебрасывая их на участок соседа... Вчерашняя работа показала, что Петя и Полина выпалывают гряду за 7 мин, Полина и Николай выпалывают её же за 14 мин, Николай и Петя — за 28 мин.
1 yesterday i had breakfast at the canteen. 2 last summer we went to the black sea. 3 he didn't call me last week. 4 why did this girl come to our office yesterday? 5 when did you buy tickets last time? 6 last june the boys played football every morning. 7 on sunday my parents were at the theatre. 8 i didn't take part at the conference last month. 9 he lived in kiev in his childhood. 10 where did he send his message? 2 трансформируйте предложения в past simplе 1 he often played chess. 2 our classes began at 9 a. m. 3 she was always busy. 4 what did you do in the evening? 5 my sister didn’t study at school, she worked at the hospital. 6 my friend prefered tea to coffee. 7 i found many stories in this magazine. 8 he was in my room, wasn't he? 9 why did you always ask so many questions? 10 jasmine seldom visited her grandparents. 3 образуйте отрицательную форму предложений 1 in summer she didn't get up early. 2 mr. white didn't write a lot of letters yesterday. 3 on friday they weren't at the station. 4 we didn't enjoy our time in rome. 5 they didn't watch a football match last weekend. 6 the girl didn't open a box at once. 7 i didn't leave my keys on the table. 8 the engineer didn't go on business trip on monday. 9 my friend didn't want to move to another flat. 10 i didn't find a surprise in the present-box. 4 поставьте вопросы к предложениям. 1 he learned english at school. (where? what language? why? or …? ) where did he learn english? what language did he learn? why did he learn english? did he learn english or french? 2 the train was five hours late. (what? why? ) what was 5 hours late? why was the train five hours late? 3 i was going to stay at my aunt’s in the crimea. (where? who? or …? ) where was i going to stay in the crimea? who was going to stay at the aunt's in the crimea? was i going to stay at my aunt's or in the hotel in the crimea? 4 they stayed in moscow only for two days. (why? where? how long? ) why did they stay in m only for 2 days? where did they stay? how long did they stay in m? 5 i bought a very beautiful dress in this shop last weekend. (where? what? when? ) where did i buy a very beautiful dress last weekend? what did i buy in this shop last weekend? when did i buy this beautiful dress in the shop? 6 they traveled to cyprus by sea. (how? where? or …? ) how did they travel to c? where did they travel to? did they travel to c or ibiza? 7 i didn’t find your telephone number. (what? why? ) what didn't i find? why didn't i find your telephone number? 8 in his childhood he was always a leader among his friends. (what? when? who? ) what was he in his childhood? when was he a leader among his friends? who was always a leader among his friends in his childhood? 9 he caught a cold last month. (what? when? why? ) what did he catch? when did he catch a cold? why did he catch a cold? 10 we did our lessons together. (what? how? ) what did we do together? how did we do our lessons?
За 8 минут
Объяснение:
Пусть Полина одна проплывает грядку за a мин, по 1/а части в минуту.
Николай пропалывает грядку за b мин, по 1/b части в минуту.
А Петя пропалывает ту же грядку за с мин, по 1/c части в минуту.
Полина и Петя пропалывают грядку за 7 минут, по 1/7 части в минуту.
1/a + 1/c = 1/7
Полина и Николай - за 14 минут, по 1/14 части в минуту.
1/a + 1/b = 1/14
А Николай и Петя делают это за 28 минут, по 1/28 части в минуту.
1/b + 1/c = 1/28
Получили систему из 3 уравнений с 3 неизвестными.
Сложим все три уравнения
1/a + 1/c + 1/a + 1/b + 1/b + 1/c = 1/7 + 1/14 + 1/28
2/a + 2/b + 2/c = 4/28 + 2/28 + 1/28 = 7/28 = 1/4
Делим всё на 2
1/a + 1/b + 1/c = 1/8
Втроём они за 1 час делают 1/8 часть грядки.
Всю грядку они прополют за 8 минут.
Можно посчитать и производительность каждого в отдельности.
Полина прополет грядку за:
1/a = (1/a + 1/b + 1/c) - (1/b + 1/c) = 1/8 - 1/28 = 7/56 - 2/56 = 5/56
a = 56/5 = 11 1/5 минуты = 11 минут 12 секунд.
Николай прополет грядку за:
1/b = (1/a + 1/b + 1/c) - (1/a + 1/c) = 1/8 - 1/7 = 7/56 - 8/56 = -1/56
b = -56 минут.
Петя прополет грядку за:
1/c = (1/a + 1/b + 1/c) - (1/a + 1/b) = 1/8 - 1/14 = 7/56 - 4/56 = 3/56
c = 56/3 = 18 2/3 минуты = 18 минут 40 секунд.
Полина лучше всех, Петя чуть хуже, а Николай всё портит.