Question

Из города А в город В одновременно отправляются 2 автобуса. Скорость 1 автобуса на 10км/ч больше 2 автобуса. Через 3,5ч первый прибыл в В, а второй находился на расстоянии, равному одной шестой между городами А и В. Сколько километров составляет расстояние между городами А и В?

Answer 1

Скорость2-го автобуса  = х (км/ч)
Скорость 1-ого автобуса = (х + 10) км/ч
Расстояние, которое прошёл 1-ый автобус = (3,5х + 35) км
Это же расстояние между городами,т.к. 1-ый автобус прошёл весь путь
от города А до города В.
Расстояние, которое прошёл 2-ой автобус = 3,5х км
1/6 расстояния  = (3,5х + 35) / 6
Составим уравнение:
 3,5х + 35 - 3,5х = (3,5х + 35) / 6
3,5х - 3,5х  + 35 = (3,5х +35)/6        общий знаменатель 6
21х - 21х + 210 = 3,5х + 35
- 3,5х = -210 + 35
  3,5х = 175
       х = 50
3,5х + 35 = 175 + 35 = 210
Ответ: 210 км - расстояние между городами А и В.

Answer 2

Problem Analysis

We are given that two buses, A and B, depart from city A to city B simultaneously. The speed of bus A is 10 km/h faster than the speed of bus B. After 3.5 hours, bus A arrives in city B, while bus B is located at a distance equal to one-sixth of the total distance between city A and city B. We need to find the total distance between city A and city B.

Solution

Let's assume the speed of bus B is x km/h. Then the speed of bus A is x + 10 km/h.

We know that the distance traveled by a bus is equal to the product of its speed and time. Therefore, the distance traveled by bus A is (x + 10) * 3.5 km, and the distance traveled by bus B is x * 3.5 km.

According to the problem, after 3.5 hours, bus A arrives in city B, while bus B is located at a distance equal to one-sixth of the total distance between city A and city B. Let's denote the total distance between city A and city B as d km.

Therefore, the distance traveled by bus A is d - (1/6) * d = (5/6) * d km, and the distance traveled by bus B is (1/6) * d km.

Now we can set up an equation based on the distances traveled by the two buses:

(x + 10) * 3.5 = (5/6) * d (Equation 1)

x * 3.5 = (1/6) * d (Equation 2)

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

Solving the Equations

Let's solve the system of equations using substitution.

From Equation 2, we can express x in terms of d:

x = (1/6) * d / 3.5

Substituting this value of x into Equation 1:

((1/6) * d / 3.5 + 10) * 3.5 = (5/6) * d

Simplifying the equation:

((1/6) * d + 35) = (5/6) * d

Multiplying both sides of the equation by 6 to eliminate the fractions:

(d + 210) = 5d

Simplifying further:

210 = 4d

Dividing both sides of the equation by 4:

d = 52.5

Therefore, the total distance between city A and city B is 52.5 km.

Answer

The distance between city A and city B is 52.5 km.