Question

Два пешехода А и В отправились одновременно рано утром в город на ярмарку. Пешеход А впереди В на 7 км. Пешеход А в первый день прошел 10 км. , а в каждый следующий на 1 км. меньше. Пешеход В в первый день прошел 2 км. , а в каждый следующий на 2 км. больше. В город они прибыли одновременно. Сколько дней они были в пути?

Answer 1

1 день: 10 -2 +7 =15 км.
2 день: 9-4+15=20.
3 день: 8-6+20=22.
4 день: 7-8+22=21.
5 день: 6-10+21=17.
6 день: 5-12+17=10.
7 день: 4-14+10=0.
Ответ: За 7 дней встретились пешеходы.

Answer 2

Problem Analysis

We have two pedestrians, A and B, who set off simultaneously early in the morning to go to a fair in the city. Pedestrian A is ahead of B by 7 km. On the first day, pedestrian A walks 10 km, and each subsequent day, they walk 1 km less. Pedestrian B walks 2 km on the first day, and each subsequent day, they walk 2 km more. They both arrive in the city at the same time. We need to determine how many days they were on the road.

Solution

Let's break down the problem step by step to find the solution.

1. On the first day, pedestrian A walks 10 km, and each subsequent day, they walk 1 km less. Let's denote the number of days as x. Therefore, the distance covered by pedestrian A on the xth day is given by: - Distance covered by pedestrian A on the xth day = 10 - (x - 1) km

2. On the first day, pedestrian B walks 2 km, and each subsequent day, they walk 2 km more. Therefore, the distance covered by pedestrian B on the xth day is given by: - Distance covered by pedestrian B on the xth day = 2 + (x - 1) * 2 km

3. The total distance covered by pedestrian A after x days is the sum of the distances covered on each day. Similarly, the total distance covered by pedestrian B after x days is the sum of the distances covered on each day. We can set up the following equations: - Total distance covered by pedestrian A after x days = 10 + 9 + 8 + ... + (10 - (x - 1)) km - Total distance covered by pedestrian B after x days = 2 + 4 + 6 + ... + (2 + (x - 1) * 2) km

4. We know that pedestrian A is ahead of pedestrian B by 7 km. Therefore, we can set up the following equation: - Total distance covered by pedestrian A after x days - Total distance covered by pedestrian B after x days = 7 km

5. Now, we can solve the equation to find the value of x.

Calculation

Let's calculate the value of x using the equations derived in the solution.

Total distance covered by pedestrian A after x days: - Total distance covered by pedestrian A after x days = 10 + 9 + 8 + ... + (10 - (x - 1)) km - Using the formula for the sum of an arithmetic series, we can simplify this expression to: - Total distance covered by pedestrian A after x days = (x / 2) * (10 + (10 - (x - 1))) km

Total distance covered by pedestrian B after x days: - Total distance covered by pedestrian B after x days = 2 + 4 + 6 + ... + (2 + (x - 1) * 2) km - Using the formula for the sum of an arithmetic series, we can simplify this expression to: - Total distance covered by pedestrian B after x days = (x / 2) * (2 + (2 + (x - 1) * 2)) km

Equation: - (x / 2) * (10 + (10 - (x - 1))) - (x / 2) * (2 + (2 + (x - 1) * 2)) = 7

Simplifying the equation: - (x / 2) * (20 - x + 1) - (x / 2) * (4 + 2x - 2) = 7 - (x / 2) * (21 - x) - (x / 2) * (2x + 2) = 7 - (x / 2) * (21 - x - 2x - 2) = 7 - (x / 2) * (19 - 3x) = 7 - (x / 2) * (19 - 3x) = 7 - 19x/2 - (3x^2)/2 = 7 - 19x - 3x^2 = 14 - 3x^2 - 19x + 14 = 0

Using the quadratic formula: - x = (-b ± sqrt(b^2 - 4ac)) / (2a) - x = (-(-19) ± sqrt((-19)^2 - 4 * 3 * 14)) / (2 * 3) - x = (19 ± sqrt(361 - 168)) / 6 - x = (19 ± sqrt(193)) / 6

Calculating the value of x: - x ≈ 4.19 or x ≈ 0.81

Since the number of days cannot be a fraction, we can conclude that they were on the road for approximately 4 days.

Answer

They were on the road for approximately 4 days.