Question

Экскурсанты за день прошли 19,6 км. С утра они шли 5 часов, а после обеда еще 3 часа. Сколько км прошли они утром, если после обеда их скорость снизилась на 2 км ч. С какой скоростью они шли утром

Answer 1

Problem Analysis

The tourists walked a total of 19.6 km in a day. They walked for 5 hours in the morning and 3 hours after lunch. The speed of the tourists decreased by 2 km/h after lunch. We need to find out how many kilometers they walked in the morning and at what speed they were walking.

Solution

Let's assume the speed of the tourists in the morning was x km/h. After lunch, their speed decreased by 2 km/h, so their speed in the afternoon was (x - 2) km/h.

To find the distance they walked in the morning, we can use the formula: distance = speed × time.

The distance they walked in the morning can be calculated as follows: distance in the morning = speed in the morning × time in the morning.

The distance they walked in the afternoon can be calculated as follows: distance in the afternoon = speed in the afternoon × time in the afternoon.

We know that the total distance they walked in a day is 19.6 km. Therefore, we can write the equation: distance in the morning + distance in the afternoon = total distance.

Substituting the formulas for distance and time, we get: (speed in the morning × time in the morning) + (speed in the afternoon × time in the afternoon) = total distance.

We are given that they walked for 5 hours in the morning and 3 hours in the afternoon. Substituting these values, we get: (speed in the morning × 5) + ((speed in the morning - 2) × 3) = 19.6.

Now we can solve this equation to find the speed in the morning and the distance they walked in the morning.

Let's solve the equation step by step:

1. Expand the equation: 5 × speed in the morning + 3 × speed in the morning - 6 = 19.6.

2. Combine like terms: 8 × speed in the morning - 6 = 19.6.

3. Move the constant term to the other side of the equation: 8 × speed in the morning = 19.6 + 6.

4. Simplify: 8 × speed in the morning = 25.6.

5. Divide both sides by 8 to solve for the speed in the morning: speed in the morning = 25.6 / 8.

6. Calculate the speed in the morning: speed in the morning = 3.2 km/h.

Now that we have the speed in the morning, we can calculate the distance they walked in the morning using the formula: distance = speed × time.

Substituting the values, we get: distance in the morning = 3.2 km/h × 5 hours.

Calculating the distance in the morning: distance in the morning = 16 km.

Therefore, the tourists walked 16 km in the morning at a speed of 3.2 km/h.

Answer

The tourists walked 16 km in the morning, and their speed in the morning was 3.2 km/h.