Question

Бригада кладет дорогу длинной 400м, ежедневно увеличивая норму на одно и то же число метров. За первый день положили 5 метров дороги. Сколько положили в последний день, если вся работа выполнена за 8 дней? Помогите пожалуйста!!!

Answer 1

Ответ:

105 м

Объяснение:

S=(5+5+(8-1)*d)*8/2=400

(10+7d)*4=400

10+7d=400:4=100

7d=100-10=90

d=90:7=12 6/7 м

а8=5+7d=5+7*(12+6/7)=5+100=105 м

Answer 2

Problem Analysis

We are given that a team is laying a road that is 400 meters long. The team increases the daily work rate by the same number of meters each day. On the first day, they laid 5 meters of road. We need to determine how many meters of road they laid on the last day if the entire job was completed in 8 days.

Solution

To solve this problem, we can use algebraic reasoning. Let's assume that the number of meters the team increases their daily work rate by is x.

On the first day, they laid 5 meters of road. On the second day, they laid 5 + x meters, on the third day, they laid 5 + 2x meters, and so on.

We know that the total length of the road is 400 meters, and the work is completed in 8 days. So, we can set up the following equation:

5 + (5 + x) + (5 + 2x) + ... + (5 + 7x) = 400

To simplify the equation, we can rewrite it as:

5 + 5 + 5 + ... + 5 + (x + 2x + 3x + ... + 7x) = 400

Simplifying further, we get:

40 + (1 + 2 + 3 + ... + 7)x = 400

The sum of the first n natural numbers can be calculated using the formula: sum = (n * (n + 1)) / 2. So, we can rewrite the equation as:

40 + (1 + 2 + 3 + ... + 7)x = 400 40 + (7 * 8 / 2)x = 400 40 + 28x = 400

Now, we can solve this equation to find the value of x:

28x = 400 - 40 28x = 360 x = 360 / 28 x ≈ 12.857

Therefore, the team increases their daily work rate by approximately 12.857 meters each day.

To find the number of meters of road laid on the last day, we can substitute the value of x into the equation:

5 + 7x = 5 + 7 * 12.857 5 + 90 ≈ 95

Therefore, the team laid approximately 95 meters of road on the last day.

Answer

The team laid approximately 95 meters of road on the last day if the entire job was completed in 8 days.