Question

Аня и Таня пропалывают грядку за 28 минут,а одна таня за 44 минуты.За сколько минут пропалывает грядку одна Аня.

Answer 1

Работу по прополке грядки примем за единицу (целое).
1) 1 : 28 = 1/28 - часть работы, которую выполнят обе девочки за минуту;
2) 1 : 44 = 1/44 - часть работы, которую выполнит одна Таня за минуту;
3) 1/28 - 1/44 = 11/308 - 7/308 = 4/308 = 1/77 - часть работы, которую выполнит одна Аня за минуту;
4) 1 : 1/77 = 1 * 77/1 = 77 (мин.) - время, за которое Аня прополет грядку.
Ответ: за 1 ч 17 мин.

Пояснения:
1/28 = 11/308 - доп.множ. 11
1/44 = 7/308 - доп.множ. 7
4/308 = 1/77 - сократили на 4

Answer 2

To find out how long it takes for Ania (Аня) to weed the garden on her own, we can set up a proportion based on the information given.

Let's denote the time it takes for Ania to weed the garden alone as "A" (in minutes).

We know that: Ania and Tanya together weed the garden in 28 minutes, which means their combined work rate is 1/28 of the garden per minute. So, in one minute, Ania's and Tanya's combined work rate is 1/28 of the garden.

Tanya alone weeds the garden in 44 minutes, which means her work rate is 1/44 of the garden per minute. So, in one minute, Tanya's work rate is 1/44 of the garden.

Now, we can set up the following proportion:

(Ania's work rate + Tanya's work rate) = (Ania and Tanya's combined work rate)

1/A + 1/44 = 1/28

Now, let's solve for "A":

1/A = 1/28 - 1/44 1/A = (44 - 28) / (28 * 44) 1/A = 16 / (28 * 44)

To find A, take the reciprocal of both sides:

A = (28 * 44) / 16 A = 77

So, it takes Ania 77 minutes to weed the garden on her own.