Question

Туристы за три дня проехали 460 км.Путь их в первый день относится к пути во второй день как 7:5.отношение пути туристов во второй день к пути в третий день равно 3:2.Сколько километров они проехали в первый,во второй,в третий день?

Answer 1

Пусть в первый день прошли 7х км, то во второй день 5х км.В третий день=10х/3Составим уравнени7х+5х+10х/3=46046х/3=460х=3*460/46=30Плдучаем в первый день прошли 30*7=210 кмво второй=5*30=150 кмв третий день=30*10/3=100 км

Answer 2

Problem Analysis

We are given that a group of tourists traveled a total distance of 460 km over three days. The ratio of their distance traveled on the first day to the distance traveled on the second day is 7:5, and the ratio of their distance traveled on the second day to the distance traveled on the third day is 3:2. We need to find the distances traveled on each of the three days.

Solution

Let's assume that the distance traveled on the first day is 7x km, the distance traveled on the second day is 5x km, and the distance traveled on the third day is 3y km.

According to the given information, we have the following equations: - 7x + 5x + 3y = 460 (equation 1) - the total distance traveled over three days is 460 km. - (5x) / (7x) = 7/5 (equation 2) - the ratio of the distance traveled on the first day to the distance traveled on the second day is 7:5. - (3y) / (5x) = 3/2 (equation 3) - the ratio of the distance traveled on the second day to the distance traveled on the third day is 3:2.

We can solve this system of equations to find the values of x and y, and then calculate the distances traveled on each day.

Solving the Equations

Let's solve equations 2 and 3 for x and y, respectively.

From equation 2: (5x) / (7x) = 7/5 Cross-multiplying, we get: 5 * 7x = 7 * 5x 35x = 35x This equation is true for any value of x, so we can choose any value for x.

From equation 3: (3y) / (5x) = 3/2 Cross-multiplying, we get: 2 * 3y = 3 * 5x 6y = 15x Dividing both sides by 3, we get: 2y = 5x This equation relates y to x.

Since we have two variables (x and y) and only one equation (equation 1), we need another equation to solve the system. However, we can use the relationship between x and y from equation 3 to substitute into equation 1.

Substituting 2y = 5x into equation 1, we get: 7x + 5x + 3(2y) = 460 7x + 5x + 6y = 460 12x + 6y = 460 (equation 4)

Now we have two equations: 12x + 6y = 460 (equation 4) 2y = 5x (equation 3)

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use the substitution method. Let's solve equation 3 for y in terms of x and substitute it into equation 4.

From equation 3: 2y = 5x Dividing both sides by 2, we get: y = (5/2)x

Substituting y = (5/2)x into equation 4, we get: 12x + 6(5/2)x = 460 12x + 15x = 460 27x = 460 Dividing both sides by 27, we get: x = 460/27

Now that we have the value of x, we can substitute it back into y = (5/2)x to find the value of y.

Substituting x = 460/27 into y = (5/2)x, we get: y = (5/2)(460/27)

Now we have the values of x and y, and we can calculate the distances traveled on each day.

Calculating the Distances

The distance traveled on the first day is 7x km, the distance traveled on the second day is 5x km, and the distance traveled on the third day is 3y km.

Substituting x = 460/27 and y = (5/2)(460/27), we can calculate the distances:

Distance traveled on the first day: 7x = 7(460/27) km

Distance traveled on the second day: 5x = 5(460/27) km

Distance traveled on the third day: 3y = 3[(5/2)(460/27)] km

Let's calculate these distances.

Calculation

Distance traveled on the first day: 7x = 7(460/27) km = 1190/9 km ≈ 132.22 km

Distance traveled on the second day: 5x = 5(460/27) km = 2300/27 km ≈ 85.19 km

Distance traveled on the third day: 3y = 3[(5/2)(460/27)] km = 3450/27 km ≈ 127.78 km

Answer

The tourists traveled approximately 132.22 km on the first day, 85.19 km on the second day, and 127.78 km on the third day.

Note: The distances are approximate due to rounding in the calculations.