Question

Группа школьников выехала на экспедицию из города А в город В на автобусе, а вернулась в город А по железной дороге, затратив на обратный путь на 30 минут больше, чем на путь в город В. Найдите скорость поезда, если она на 20 километров в час меньше скорости автобуса, длинна шоссе между городами А и В состовляет 160 километров, а длинна железной дороги-150 километров.

Answer 1

((160)/(х+20)) + 0.5 = (150)/х
где х - скорость поезда
тогда х=60

Answer 2

Problem Analysis

A group of school students traveled from city A to city B by bus and returned from city B to city A by train. The return journey took 30 minutes longer than the journey to city B. We need to find the speed of the train if it is 20 kilometers per hour slower than the speed of the bus. The distance between city A and city B is 160 kilometers by road and 150 kilometers by train.

Solution

Let's assume the speed of the bus is x kilometers per hour. Therefore, the speed of the train is x - 20 kilometers per hour.

To find the time taken for the journey from city A to city B by bus, we can use the formula:

Time = Distance / Speed

The time taken for the journey from city A to city B by bus is:

Time(bus) = Distance(road) / Speed(bus) = 160 / x

The time taken for the return journey from city B to city A by train is:

Time(train) = Distance(train) / Speed(train) = 150 / (x - 20)

According to the problem, the return journey took 30 minutes longer than the journey to city B. We can convert 30 minutes to hours by dividing by 60:

30 minutes = 30 / 60 = 0.5 hours

Therefore, we can set up the equation:

Time(train) = Time(bus) + 0.5

Substituting the values we have:

150 / (x - 20) = 160 / x + 0.5

To solve this equation, we can cross-multiply and simplify:

150x = 160(x - 20) + 0.5x(x - 20)

Simplifying further:

150x = 160x - 3200 + 0.5x^2 - 10x

Rearranging the equation:

0.5x^2 - 10x - 3200 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 0.5, b = -10, and c = -3200.

Solving the equation will give us two possible values for x, but we will only consider the positive value since speed cannot be negative.

Let's calculate the value of x using the quadratic formula.

Calculation

Using the quadratic formula:

x = (-(-10) ± √((-10)^2 - 4 * 0.5 * -3200)) / (2 * 0.5)

Simplifying:

x = (10 ± √(100 + 6400)) / 1

x = (10 ± √6500) / 1

Calculating the square root of 6500:

√6500 ≈ 80.622577

Substituting the value of √6500:

x = (10 ± 80.622577) / 1

Calculating the positive value of x:

x = (10 + 80.622577) / 1 ≈ 90.622577

Therefore, the speed of the bus is approximately 90.622577 kilometers per hour.

Since the speed of the train is 20 kilometers per hour slower than the speed of the bus, the speed of the train is:

Speed(train) = Speed(bus) - 20 ≈ 90.622577 - 20 ≈ 70.622577

Therefore, the speed of the train is approximately 70.622577 kilometers per hour.

Answer

The speed of the train is approximately 70.622577 kilometers per hour.