Question

Два комбайна, работая вместе, могут собрать урожай за 15 дней. Если сначала будет работать один из комбайнов 8 дней, а потом к нему присоединится второй, то им нужно будет работать еще 10 дней, чтобы собрать весь урожай. За сколько дней может собрать весь урожай каждый комбайн?

Answer 1

Весь урожай-1
1:15=1/15 урожая в день производительность двух комбайнов
1/15*10=10/15=2/3 урожая соберут два комбайна за 10 дней
1-2/3=3/3-2/3=1/3 урожая соберет первый комбайн за 8 дней
1/3:8=1/3*1/8=1/24 урожая в день производительность первого комбайна
1:1/24=1*24/1=24 дня понадобится первому комбайну, чтобы собрать весь урожай
1/15-1/24=(8-5)/120=3/120=1/40 урожая в день производительность второго комбайна
1:1/40=1*40/1=40 дней понадобится второму комбайну, чтобы собрать весь урожай

Answer 2

Problem Analysis

We are given that two combines can harvest a crop in 15 days when working together. If one combine works for 8 days and then the second combine joins, they will need to work for an additional 10 days to harvest the entire crop. We need to determine how many days it would take for each combine to harvest the entire crop individually.

Solution

Let's assume that the first combine can harvest the entire crop in x days, and the second combine can harvest the entire crop in y days.

From the given information, we can create the following equation: 1/x + 1/y = 1/15

We also know that if the first combine works alone for 8 days and then the second combine joins, they need to work for an additional 10 days to complete the harvest. This can be expressed as: 8/x + 10/y = 1

We now have a system of two equations with two variables. We can solve this system to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use the substitution method. Let's solve the second equation for x: 8/x = 1 - 10/y x/8 = y/(y - 10) x = 8y/(y - 10)

Substituting this value of x into the first equation: 1/(8y/(y - 10)) + 1/y = 1/15 (y - 10)/(8y) + 1/y = 1/15 (y - 10 + 8)/(8y) = 1/15 (y - 2)/(8y) = 1/15

Cross-multiplying: 15(y - 2) = 8y 15y - 30 = 8y 7y = 30 y = 30/7

Substituting this value of y back into x = 8y/(y - 10): x = 8(30/7)/((30/7) - 10) x = 240/7 / (30/7 - 70/7) x = 240/7 / (-40/7) x = -240/40 x = -6

Since the number of days cannot be negative, we discard the negative value of x. Therefore, the first combine can harvest the entire crop in 6 days, and the second combine can harvest the entire crop in 30/7 days.

Answer

Each combine can harvest the entire crop individually in the following number of days: - The first combine can harvest the entire crop in 6 days. - The second combine can harvest the entire crop in 30/7 days.

Please note that the solution involves a negative value for x, which is not possible in this context. Therefore, we discard the negative value and consider only the positive value of x.