Question

Реши задачу двумя способами. Ученик 6 класса на компьютере за 2 часа набрал 6 страниц, а ученик 7 класса за 1 час на 2 страницы больше, чем шестиклассник за 1 час. За сколько часов наберут на компьютере ученики 160 страниц работая вместе. Заранее спасибо.

Answer 1

1.
6:2=3 стр. в час (шестиклассник)
3+2=5 в час семиклассник
3+5=8 в час вместе
160:8=20 часов затратят
2.
Т.к. 6-ник за два часа набрал 6 страниц, а 7-ник за час на 2 стр. больше, то мы можем предположить, что за два часа он набрал на 4 больше.
6+4=10 7-ник набрал страниц
10+6=16 страниц за два часа
160:16=10
10*2=20 часов

Answer 2

Problem Analysis

We are given that a 6th-grade student can type 6 pages on a computer in 2 hours, and a 7th-grade student can type 2 pages more than the 6th-grade student in 1 hour. We need to determine how many hours it will take for the students to type a total of 160 pages when working together.

Solution 1: Using Proportions

Let's assume that the 6th-grade student types x pages per hour. According to the given information, the 7th-grade student types (x + 2) pages per hour.

We can set up the following proportion to find the value of x:

6th-grade student's typing rate: 6 pages / 2 hours = x pages / 1 hour

Simplifying the proportion, we get:

6 / 2 = x / 1

Cross-multiplying, we find:

2x = 6

Dividing both sides by 2, we get:

x = 3

Therefore, the 6th-grade student types 3 pages per hour, and the 7th-grade student types (3 + 2) = 5 pages per hour.

Now, let's determine how many hours it will take for the students to type a total of 160 pages when working together. We can set up the following equation:

Total pages typed = (6th-grade student's typing rate + 7th-grade student's typing rate) * time

Substituting the values we found earlier, we get:

160 = (3 + 5) * time

Simplifying the equation, we have:

160 = 8 * time

Dividing both sides by 8, we find:

time = 20

Therefore, it will take the students 20 hours to type a total of 160 pages when working together.

Solution 2: Using Rates

Alternatively, we can solve the problem using rates. We know that the 6th-grade student types 6 pages in 2 hours, which means their typing rate is 6 pages / 2 hours = 3 pages per hour.

Similarly, the 7th-grade student types 2 pages more than the 6th-grade student in 1 hour. So their typing rate is 3 + 2 = 5 pages per hour.

To find the total time it will take for the students to type 160 pages when working together, we can set up the following equation:

Total pages typed = (6th-grade student's typing rate + 7th-grade student's typing rate) * time

Substituting the values we found earlier, we get:

160 = (3 + 5) * time

Simplifying the equation, we have:

160 = 8 * time

Dividing both sides by 8, we find:

time = 20

Therefore, it will take the students 20 hours to type a total of 160 pages when working together.

Answer

The students will take 20 hours to type a total of 160 pages when working together.