Question

На плантации винограда шла уборка урожая. Одна группа виноградарей работала 6 ч., а другая — 8 ч. Выяснилось, что обе группы собрали одинаковое количество винограда. Найди количество центнеров винограда, которое убрала первая группа виноградарей за 6 ч., если известно, что каждый час она убирала на 20 ц больше второй группы.

Answer 1

Ответ:

480 ц

Объяснение:

пусть первая группа убирала х ц в час

тогда вторая группа убирала х-20  ц в час

за 6 часов первая группа собрала 6х

за 8 часов вторая группа собрала 8(х-20)

составим уравнение

так как обе группы собрали одинаковое количество винограда то

6х=8(х-20)

6х=8х-160

8х-6х=160

2x=160

x=160/2=80

6x=6*80=480 центнеров винограда убрала первая группа виноградарей за 6 ч

Answer 2

Problem Analysis

We are given two groups of grape pickers working on a vineyard. One group works for 6 hours, while the other group works for 8 hours. Both groups collect the same amount of grapes. We need to find the number of hundredweights of grapes that the first group collected in 6 hours, knowing that each hour they collected 20 hundredweights more than the second group.

Solution

Let's assume that the second group collected x hundredweights of grapes in 1 hour. Therefore, the first group collected (x + 20) hundredweights of grapes in 1 hour.

Since the first group worked for 6 hours, the total number of hundredweights of grapes they collected can be calculated as follows:

Total grapes collected by the first group = (x + 20) * 6

Similarly, the second group worked for 8 hours, so the total number of hundredweights of grapes they collected can be calculated as follows:

Total grapes collected by the second group = x * 8

According to the problem statement, both groups collected the same amount of grapes. Therefore, we can set up the following equation:

(x + 20) * 6 = x * 8

Now, let's solve this equation to find the value of x and then calculate the total grapes collected by the first group.

Calculation

Expanding the equation, we get:

6x + 120 = 8x

Rearranging the equation, we get:

8x - 6x = 120

Simplifying, we get:

2x = 120

Dividing both sides by 2, we get:

x = 60

Now, substituting the value of x back into the equation, we can find the total grapes collected by the first group:

Total grapes collected by the first group = (x + 20) * 6 = (60 + 20) * 6 = 80 * 6 = 480 hundredweights

Therefore, the first group of grape pickers collected 480 hundredweights of grapes in 6 hours.

Answer

The first group of grape pickers collected 480 hundredweights of grapes in 6 hours.

Explanation

The problem states that the first group collected grapes at a rate of 20 hundredweights per hour more than the second group. By setting up an equation and solving it, we found that the second group collected grapes at a rate of 60 hundredweights per hour. Therefore, the first group collected grapes at a rate of 80 hundredweights per hour. Multiplying this rate by the number of hours worked (6), we found that the first group collected a total of 480 hundredweights of grapes.