Question

СРОЧНО! 40 баллов! Два туриста вышли одновременно из пунктов A и B навстречу друг другу. Скорость движения первого туриста на 1 км/ч больше скорости второго. Первый турист пришел в пункт B на 48 мин раньше, чем второй турист - в пункт A. Найдите скорости движения туристов, если расстояние между пунктами A и B равно 24 км.

Answer 1

Problem Analysis

We have two tourists who start simultaneously from points A and B and move towards each other. The speed of the first tourist is 1 km/h faster than the speed of the second tourist. The first tourist arrives at point B 48 minutes earlier than the second tourist arrives at point A. The distance between points A and B is 24 km. We need to find the speeds of the two tourists.

Solution

Let's assume the speed of the second tourist is x km/h. Then the speed of the first tourist is x + 1 km/h.

We know that the time taken by the first tourist to travel from point A to point B is 48 minutes less than the time taken by the second tourist to travel from point B to point A.

Let's calculate the time taken by each tourist to travel their respective distances.

The time taken by the first tourist to travel from point A to point B is given by: time_AB = distance_AB / speed_first_tourist

The time taken by the second tourist to travel from point B to point A is given by: time_BA = distance_BA / speed_second_tourist

We can set up the following equation based on the given information: time_AB = time_BA - 48 minutes

Since the distance between points A and B is 24 km, we have: distance_AB = distance_BA = 24 km

Substituting the values, we get: 24 / (x + 1) = 24 / x - 48 minutes

To simplify the equation, we can convert 48 minutes to hours by dividing it by 60: 24 / (x + 1) = 24 / x - 0.8 hours

Now, let's solve the equation to find the value of x.

Calculation

To solve the equation, we can cross-multiply and simplify: 24x = 24(x + 1) - 0.8x(x + 1)

Expanding and simplifying further: 24x = 24x + 24 - 0.8x^2 - 0.8x

Combining like terms: 0 = -0.8x^2 - 0.8x + 24

Dividing the equation by -0.8 to simplify: 0 = x^2 + x - 30

Now, we can solve this quadratic equation to find the value of x.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 1, and c = -30.

Substituting the values, we get: x = (-1 ± √(1^2 - 4(1)(-30))) / (2(1))

Simplifying further: **x = (-1 ±