Question

Помощь плиз!!! Турист пройдя 6км, увеличил скорость на 2км/ч и прошёл ещё 3км. Найдите первоначальную скорость туриста, если он на весь путь потратил 2ч.​

Answer 1

Обозначим первоначальную скорость пешехода как х км/ч, тогда на первый участок пути он потратил (6/x) часов, потом его скорость стала (х+2)км/ч, и на второй участок пути он потратил (3/(x+2)) часов. Всего он потратил 2 часа, составим и решим уравнение:

6/x + 3/(x+2) = 2    /домножим

6/x * (x+2) + 3/(x+2) * x = 2 * x * (x+2) это действие не пишется, оно здась, чтобы показать что и на что домножаем.

6(x+2) + 3x = 2x(x+2)

6x + 12 + 3x = 2x² + 4x

-2x² +5x + 12 = 0

2x² - 5x - 12 = 0

D = b² - 4ac = 25 + 4*24 = 25 + 96 = 121 (11²)

x₁ = (-b + √D)/2a = (5 + 11)/4 = 16 / 4 = 4

x₂ = (-b - √D)/2a = (5 - 11)/4 = -6 / 4 = -1,5 -- не удовлетворяет условиям задачи.

Ответ: изначальная скорость пешехода была 4 км/ч

Answer 2

Calculation of Initial Speed

To find the initial speed of the tourist, we can use the formula:

Distance = Speed × Time

Let's break down the information given in the problem:

- The tourist walked 6 km initially. - Then, the tourist increased their speed by 2 km/h and walked an additional 3 km. - The total time taken for the entire journey was 2 hours.

Let's assume the initial speed of the tourist is x km/h.

Using the formula, we can calculate the time taken for the initial 6 km:

6 km = x km/h × t1

where t1 is the time taken for the initial 6 km.

Next, let's calculate the time taken for the additional 3 km:

3 km = (x + 2) km/h × t2

where t2 is the time taken for the additional 3 km.

We know that the total time for the entire journey is 2 hours:

t1 + t2 = 2 hours

Now, let's solve these equations to find the initial speed of the tourist.

From the first equation, we can express t1 in terms of x:

t1 = 6 km / x km/h

From the second equation, we can express t2 in terms of x:

t2 = 3 km / (x + 2) km/h

Substituting these values into the third equation, we get:

6 km / x km/h + 3 km / (x + 2) km/h = 2 hours

To solve this equation, we can multiply through by x(x + 2) to eliminate the denominators:

6(x + 2) + 3x = 2x(x + 2)

Simplifying the equation:

6x + 12 + 3x = 2x^2 + 4x

2x^2 - 5x - 12 = 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 = 2, b = -5, and c = -12.

Solving the equation, we find two possible values for x: -1.5 and 4.

However, since speed cannot be negative, the initial speed of the tourist is 4 km/h.

Therefore, the initial speed of the tourist was 4 km/h.