Question

9 Прочитай условие. Есть ли в задаче лишние данные? Реши задачу. Между городами расстояние 720 км. В 8 часов утра две группы туристов вышли из них одновременно навстречу друг другу и, двигаясь равномерно, встретились через 16 дней на рас- стоянии 320 км от первого города. Сколько километров в день проходила каждая группа? можете решить с таблицей​

Answer 1

Ответ: первая группа проходила в день 20 км, а вторая группа 25 км.

Пошаговое объяснение:  Есть ли в задаче лишние данные?

Лишнее ВРЕМЯ (вышли в 8 часов). Не имеет значения, в какое время  вышли.

320 : 16 = 20 (км) - в день  проходила одна группа

720 - 320 = 400 (км) - должна проити вторая группа

400 : 16 = 25 (км) - в день проходила другая  группа

Answer 2

Analyzing the Problem

The problem involves two groups of tourists traveling towards each other from two different cities. The distance between the cities is 720 km. The two groups start simultaneously and meet after 16 days at a point 320 km from the first city. We need to find out the daily distance covered by each group.

Identifying Relevant Information

The given information includes: 1. Distance between the cities: 720 km 2. Time taken to meet: 16 days 3. Distance from the first city at the time of meeting: 320 km

Determining Daily Distance Covered

To find the daily distance covered by each group, we can use the formula: \[ \text{Total distance} = \text{Speed} \times \text{Time} \]

Let's denote the speed of the first group as \( x \) km/day and the speed of the second group as \( y \) km/day.

Solving the Problem

We can set up a system of equations to solve for the speeds of the two groups.

1. The total distance covered by both groups in 16 days is 720 km: \[ 16x + 16y = 720 \]

2. At the time of meeting, the combined distance covered by both groups is 320 km: \[ 16x + 16y = 320 \]

We can solve this system of equations to find the daily distance covered by each group.

Solution

Using the system of equations, we can solve for the daily distance covered by each group: \[ 16x + 16y = 720 \] \[ x + y = 45 \]

Solving for \( x \) and \( y \), we find: \[ x = 25 \, \text{km/day} \] \[ y = 20 \, \text{km/day} \]

Therefore, each group covered 25 km/day and 20 km/day, respectively.