Question

В турпоходе дежурным оле и юле нужно почистить кастрюлю картофеля. оля с этим справляется за 15 минут одна , юля за 18 минут одна. сумеют ли они почистить кастрюлю картофеля за 10 минут если будут работать вместе

Answer 1

Примем всю работу за 1.
1:15=1/15 кастрюли в минуту - производительность Оли.
1:18=1/18 кастрюли в минуту - производительность Юли.
1/15 + 1/18 = 6/90 + 5/90 = 11/90 кастрюли в минуту - общая производительность Оли и Юли.
1 : (11/90) = 1 * (90/11) = 90/11 = 8 целых 2/11 минуты - за такое время девочки начистят кастрюлю картошки, работая вместе.
8 целых 2/11 минуты < 10 минут
Ответ: да, успеют.

Answer 2

Problem Statement

Оле и Юле нужно почистить кастрюлю картофеля. Оля справляется с этим за 15 минут, а Юля за 18 минут. Вопрос: смогут ли они почистить кастрюлю картофеля за 10 минут, если будут работать вместе?

Solution

To determine if Olga and Julia can peel the pot of potatoes in 10 minutes, we need to calculate their combined peeling rate.

Let's assume that the amount of work required to peel the pot of potatoes is represented by the variable "W". Olga's peeling rate is 1/15 of the work per minute, and Julia's peeling rate is 1/18 of the work per minute.

To find their combined peeling rate, we can add their individual rates together:

Olga's rate: 1/15 of the work per minute. Julia's rate: 1/18 of the work per minute.

Their combined rate is the sum of their individual rates:

Combined rate = Olga's rate + Julia's rate.

Now, let's calculate their combined rate:

Combined rate = 1/15 + 1/18.

To add these fractions, we need to find a common denominator. The least common multiple of 15 and 18 is 90.

So, let's rewrite the fractions with a common denominator of 90:

Combined rate = (1/15) * (6/6) + (1/18) * (5/5).

Simplifying the fractions:

Combined rate = 6/90 + 5/90.

Adding the fractions:

Combined rate = (6 + 5)/90.

Combined rate = 11/90.

Therefore, Olga and Julia's combined peeling rate is 11/90 of the work per minute.

To determine if they can peel the pot of potatoes in 10 minutes, we need to calculate the amount of work they can do together in 10 minutes.

Work done in 10 minutes = Combined rate * 10.

Work done in 10 minutes = (11/90) * 10.

Simplifying the fraction:

Work done in 10 minutes = 11/9.

Since the work done in 10 minutes is greater than the total amount of work required (which is represented by the variable "W"), we can conclude that Olga and Julia can peel the pot of potatoes in 10 minutes if they work together.

Therefore, yes, they will be able to peel the pot of potatoes in 10 minutes if they work together.