Question

Розв*язати задачу за допомогою рівняння: Щоб потрапити із села до міста,потрібно пройти 19км.Першу частину шляху турист пройшов за 2 год., а другу-за 3 год.,причому його швидкість на першій ділянці була на 2 км/год більшою,ніж на другій.Знайдіть швидкість туриста на другій ділянці шляху.

Answer 1

Нехай X+2км/год - шв-ть на 1 ділянці,

тоді X - шв-ть на 2 ділянці

Одержимо рівняння 2(X+2)+3*X= 19

2x+4+3x=19

5x=19-4

5x=15

x=3

Відповідь: 3км/год.

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the tourist on the second part of the journey. We are given that the total distance is 19 km, and the tourist took 2 hours to cover the first part and 3 hours to cover the second part. The speed on the first part is 2 km/h greater than the speed on the second part.

Solution

Let's assume the speed on the second part of the journey is x km/h. Since the speed on the first part is 2 km/h greater, the speed on the first part is (x + 2) km/h.

We can use the formula speed = distance / time to calculate the speeds on each part of the journey.

For the first part: speed = distance / time speed = (x + 2) km/h time = 2 hours distance = 19 km (total distance) - distance on the second part

For the second part: speed = distance / time speed = x km/h time = 3 hours distance = distance on the second part

To find the distance on the second part, we can subtract the distance on the first part from the total distance: distance on the second part = total distance - distance on the first part distance on the second part = 19 km - (x + 2) km/h * 2 hours

Now we can set up an equation using the formula speed = distance / time for each part of the journey:

For the first part: (x + 2) km/h = (19 km - (x + 2) km/h * 2 hours) / 2 hours

For the second part: x km/h = (19 km - (x + 2) km/h * 2 hours) / 3 hours

Simplifying these equations will allow us to solve for x, which represents the speed on the second part of the journey.

Calculation

Let's solve the equations to find the value of x.

Equation 1: (x + 2) km/h = (19 km - (x + 2) km/h * 2 hours) / 2 hours

Simplifying: (x + 2) km/h = (19 km - 2(x + 2) km/h) / 2 hours

Multiplying both sides by 2 hours to eliminate the denominator: 2(x + 2) km = 19 km - 2(x + 2) km

Expanding and simplifying: 2x + 4 km = 19 km - 2x - 4 km

Combining like terms: 4x + 4 km = 19 km - 4 km

Simplifying further: 4x + 4 km = 15 km

Subtracting 4 km from both sides: 4x = 11 km

Dividing both sides by 4: x = 11 km / 4

Equation 2: x km/h = (19 km - (x + 2) km/h * 2 hours) / 3 hours

Substituting the value of x from Equation 1: x km/h = (19 km - ((11 km / 4) + 2) km/h * 2 hours) / 3 hours

Simplifying: x km/h = (19 km - (11 km / 4 + 8/4) km/h * 2 hours) / 3 hours

Simplifying further: x km/h = (19 km - (11 km + 8 km) / 4 km/h * 2 hours) / 3 hours

Simplifying the numerator: x km/h = (19 km - 19 km / 4 km/h * 2 hours) / 3 hours

Multiplying 19 km by 2 hours: x km/h = (19 km - 38 km / 4 km/h) / 3 hours

Simplifying further: x km/h = (19 km - 9.5 km/h) / 3 hours

Subtracting 9.5 km from 19 km: x km/h = 9.5 km / 3 hours

Dividing 9.5 km by 3 hours: x = 3.1667 km/h

Answer

The speed of the tourist on the second part of the journey is approximately 3.1667 km/h.

Please note that the calculations were rounded to four decimal places for simplicity.