Question

Петя может съесть торт за 9 минут, а Алена- за 11 минут. Какая часть торта останется через одну минуту,если дети начнут его есть вместе?

Answer 1

Петя за 1 минуту съедает 1/9 торта
Алена за 1 минуту съедает 1/11 торта
Вместе за 1 минуту они съедят 1/9+1/11=20/99 торта
останется 1-20/99=79/99 торта

Answer 2

Problem Analysis

We are given that Petya can eat a cake in 9 minutes and Alena can eat the same cake in 11 minutes. We need to determine how much of the cake will be left after one minute if they start eating it together.

Solution

To solve this problem, we can calculate the fraction of the cake that Petya and Alena can eat in one minute and subtract it from 1 to find the remaining fraction of the cake.

Let's calculate the fraction of the cake that Petya can eat in one minute. Since Petya can eat the whole cake in 9 minutes, he can eat 1/9 of the cake in one minute.

Similarly, Alena can eat 1/11 of the cake in one minute.

To find the remaining fraction of the cake after one minute, we subtract the sum of the fractions eaten by Petya and Alena from 1:

Remaining fraction = 1 - (Fraction eaten by Petya + Fraction eaten by Alena)

Let's calculate the remaining fraction:

Remaining fraction = 1 - (1/9 + 1/11)

To simplify the calculation, we can find a common denominator for 9 and 11, which is 99:

Remaining fraction = 1 - (11/99 + 9/99)

Remaining fraction = 1 - (20/99)

Remaining fraction = 79/99

Therefore, 79/99 of the cake will be left after one minute if Petya and Alena start eating it together.

Answer

If Petya can eat a cake in 9 minutes and Alena can eat the same cake in 11 minutes, then 79/99 of the cake will be left after one minute if they start eating it together.