Question

РЕШИТЕ ЗАДАЧУ С ПОМОЩЬЮ СИСТЕМЫ УРАВНЕНИЙ!! Путь длиной 240 км между пунктами A и B автомобиль прошел с постоянной скоростью. Возвращаясь обратно, он прошел половину пути с той же скоростью, а затем увеличил скорость на 10км.ч. В результате на обратный путь было затрачено на 24 мин. меньше, чем на путь от A до B. С какой скоростью ехал автомобиль из пункта A в пункт B?

Answer 1

Х - скорость от А до В 240/х = 120/х + 120/(х+10) + 2/5 240 * (х+10) = 120 * (х+10) + 120х + 0,4х * (х + 10) 240х + 2400 = 120х + 1200 + 120х + 0,4x^2 + 4x 0,4x^2 + 4x - 1200 = 0 x^2 + 10x - 3000 = 0 х1 = 50 х2 = -60 (не удовлетворяет условию) Ответ: 50 км/час

Answer 2

Problem Analysis

We are given that a car traveled a distance of 240 km between points A and B at a constant speed. On the return journey, the car traveled half the distance at the same speed and then increased its speed by 10 km/h. The total time taken for the return journey was 24 minutes less than the time taken for the journey from A to B. We need to find the speed at which the car traveled from point A to point B.

Solution

Let's assume the speed of the car from A to B is x km/h.

According to the problem, the car traveled half the distance (120 km) on the return journey at the same speed x km/h.

For the remaining half of the distance (also 120 km), the car increased its speed by 10 km/h. Therefore, the speed for this part of the journey is (x + 10) km/h.

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

Time = Distance / Speed

For the journey from A to B, the time taken is:

Time_AB = 240 km / x km/h

For the return journey, the time taken is:

Time_BA = 120 km / x km/h + 120 km / (x + 10) km/h

We are given that the time taken for the return journey was 24 minutes (or 0.4 hours) less than the time taken for the journey from A to B. Therefore, we can write the equation:

Time_AB - Time_BA = 0.4 hours

Substituting the values of Time_AB and Time_BA, we get:

(240 / x) - (120 / x + 120 / (x + 10)) = 0.4

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

Calculation

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

(240 / x) - (120 / x + 120 / (x + 10)) = 0.4

Multiplying through by x(x + 10) to eliminate the denominators:

240(x + 10) - 120x - 120(x + 10) = 0.4x(x + 10)

Simplifying the equation:

240x + 2400 - 120x - 1200 - 120x - 1200 = 0.4x^2 + 4x

0.4x^2 + 4x - 240x - 120x - 120x + 2400 - 1200 - 1200 = 0

0.4x^2 - 600x + 600 = 0

Dividing through by 0.4 to simplify the equation:

x^2 - 1500x + 1500 = 0

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

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 1, b = -1500, and c = 1500.

Substituting the values:

x = (-(-1500) ± √((-1500)^2 - 4 * 1 * 1500)) / (2 * 1)

Simplifying:

x = (1500 ± √(2250000 - 6000)) / 2

x = (1500 ± √(2244000)) / 2

x = (1500 ± 1498.57) / 2

Taking the positive value:

x = (1500 + 1498.57) / 2

x = 2998.57 / 2

x = 1499.285

Therefore, the speed at which the car traveled from point A to point B is approximately 1499.285 km/h.

Answer

The car traveled from point A to point B at a speed of approximately 1499.285 km/h.

Note: The answer has been rounded to three decimal places for simplicity.