Question

Аня и Таня пропалывают грядку за 36 мин, а одна Таня - за 117 мин. За сколько минут провалывает грядку одна Аня?

Answer 1

1)     1 : 36=1/36(часть) - пропалывают вместе за 1 мин

2)   1 : 117=1/117(часть) - пропалывает Таня за 1 мин

3)    1/36 - 1/117=13/468 - 4/468=9/468=1/52(часть) - пропалывает Аня за 1 мин

4)   1 : 1/852=52(мин) - потребуется Ане

Answer 2

Let's assume that the rate at which they weed the garden is constant. We can use the concept of "work" to solve this problem.

Let's denote the time it takes for one Anya to weed the garden as "A" (in minutes), and the time it takes for one Tanya to weed the garden as "T" (in minutes).

We know that when both Anya and Tanya work together, they complete the task in 36 minutes. This means that their combined rate of work is the sum of their individual rates.

So, the combined rate is given by: 1/A + 1/T = 1/36

We also know that Tanya takes 117 minutes to weed the garden alone, so her rate of work is: 1/T = 1/117

Now, we can use the information above to find the rate of work of Anya alone. Substituting the value of 1/T into the equation for the combined rate: 1/A + 1/117 = 1/36

Now, let's solve for 1/A: 1/A = 1/36 - 1/117

To simplify the right side of the equation, find a common denominator for 36 and 117, which is 468: 1/A = (13 - 4) / 468 1/A = 9 / 468

Now, invert both sides to find the value of A: A = 468 / 9 A = 52

Therefore, it takes one Anya 52 minutes to weed the garden alone.