Question

В турпоходе дежурные оля и юля должны очистить кастрюлю картофеля. Оля одна может справиться с этой работой за 15 мин, Юля за 18 мин. Успеют ли они начистить кастрюлю картофеля за 10 мин, 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 Analysis

In this scenario, Olga (Оля) and Julia (Юля) are on a hiking trip and need to clean a pot of potatoes. Olga can clean the pot by herself in 15 minutes, while Julia can do it in 18 minutes. The question is whether they will be able to clean the pot together in 10 minutes.

Solution

To determine if Olga and Julia can clean the pot together in 10 minutes, we need to calculate their combined cleaning rate.

Let's start by finding the individual cleaning rates of Olga and Julia. We can calculate the rate by dividing the amount of work (cleaning the pot) by the time taken.

Olga's cleaning rate: 1 pot / 15 minutes Julia's cleaning rate: 1 pot / 18 minutes

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

Combined cleaning rate: 1 pot / 15 minutes + 1 pot / 18 minutes

To simplify the calculation, we can find the least common multiple (LCM) of 15 and 18, which is 90. This means that Olga and Julia's combined cleaning rate is:

Combined cleaning rate: 6 pots / 90 minutes + 5 pots / 90 minutes

Now, let's calculate the combined cleaning rate:

Combined cleaning rate: 11 pots / 90 minutes

This means that Olga and Julia can clean 11 pots together in 90 minutes.

To determine if they can clean the pot in 10 minutes, we can calculate their cleaning rate per minute:

Cleaning rate per minute: 11 pots / 90 minutes = 0.122 pots/minute

Now, let's calculate how many pots they can clean in 10 minutes:

Pots cleaned in 10 minutes: 0.122 pots/minute * 10 minutes = 1.22 pots

Since they can clean 1.22 pots in 10 minutes, it is not possible for them to clean the entire pot of potatoes together in that time.

Conclusion

Olga and Julia will not be able to clean the pot of potatoes together in 10 minutes. Their combined cleaning rate allows them to clean approximately 1.22 pots in 10 minutes, which is less than the total amount of work required.