Question

Экскурсанты за день прошли 8,6 км. С утра они шли 3 час(-а), а после обеда — ещё 1 час(-а). Сколько километров экскурсанты прошли утром, если после обеда их скорость снизилась на 1 км/ч. С какой скоростью шли экскурсанты утром?

Answer 1

Ответ:

2,4 км/ч

Пошаговое объяснение:

х км/ч - скорость после обеда

х + 1 - скорость до обеда

3 (х +1) + х = 8,6

3х + 3 + х = 8,6

4х + 3 = 8,6

4х = 8,6 - 3

4х = 5,6

х = 5,6 : 4 = 1,4 км/ч - скорость после обеда

1,4 + 1 = 2,4 км/ ч - скорость до обеда

Проверка:

3 · 2,4 + 1,4 = 7,2 + 1,4 = 8,6 - верно

Answer 2

Problem Analysis

We are given that a group of tourists walked a total of 8.6 km in a day. They walked for 3 hours in the morning and 1 hour after lunch. The speed of the tourists decreased by 1 km/h after lunch. We need to find out how many kilometers the tourists walked in the morning and at what speed they were walking.

Solution

Let's assume that the speed of the tourists in the morning was x km/h. After lunch, their speed decreased by 1 km/h, so their speed in the afternoon was (x - 1) km/h.

We know that the total distance covered by the tourists in a day is 8.6 km. We can set up the following equation to represent this:

Distance covered in the morning + Distance covered in the afternoon = Total distance covered

Let's solve this equation to find the distance covered in the morning.

Calculating the Distance Covered in the Morning

The distance covered in the morning can be calculated by multiplying the speed in the morning (x) by the time spent walking in the morning (3 hours):

Distance covered in the morning = Speed in the morning × Time spent walking in the morning

Substituting the given values, we have:

Distance covered in the morning = x km/h × 3 hours

Calculating the Distance Covered in the Afternoon

The distance covered in the afternoon can be calculated by multiplying the speed in the afternoon ((x - 1)) by the time spent walking in the afternoon (1 hour):

Distance covered in the afternoon = Speed in the afternoon × Time spent walking in the afternoon

Substituting the given values, we have:

Distance covered in the afternoon = (x - 1) km/h × 1 hour

Solving the Equation

Now, let's substitute the calculated distances into the equation:

Distance covered in the morning + Distance covered in the afternoon = Total distance covered

x km/h × 3 hours + (x - 1) km/h × 1 hour = 8.6 km

Simplifying the equation:

3x + x - 1 = 8.6

4x - 1 = 8.6

4x = 9.6

x = 2.4

Therefore, the speed of the tourists in the morning was 2.4 km/h.

To find the distance covered in the morning, we can substitute the calculated speed into the equation:

Distance covered in the morning = Speed in the morning × Time spent walking in the morning

Distance covered in the morning = 2.4 km/h × 3 hours

Distance covered in the morning = 7.2 km

Therefore, the tourists covered 7.2 km in the morning.

Summary

The tourists covered a distance of 7.2 km in the morning, and their speed in the morning was 2.4 km/h.