Question

Из пункта А в пункт В, расетояние между которыми 280 км, одновременно пиехали автомобилист и мотоциклист. Известно, что в час автомобилист проезжает на 20 км больше, чем мотоциклист. Определите скорость мотоциклиста, если известно, что он прибыл в пункт В на 15 минут позже ав-томобилиста.

Answer 1

Объяснение:

15 мин=1/4 часа.

Пусть скорость мотоциклиста равна х км/ч (x>0).           ⇒

Скорость автомобилиста равна (х+20) км/ч.

$\displaystyle\\\frac{280}{x} -\frac{280}{x+20} =\frac{1}{4} \\\\280*4*(x+20)-280*4*x=x*(x+20)\\\\1120*(x+20)-1120*x=x^2+20x\\\\1120x+22400-1120x=x^2+20x\\\\x^2+20x-22400=0\\\\x^2-140x+160x-22400=0\\\\x*(x-140)+160*(x-140)=0\\\\(x-140)*(x+160)=0\\\\x=140=0\\\\x_1=140.\\\\x+160=0\\\\x_2=-160\notin.$

Ответ: скорость мотоциклиста равна 140 км/ч.

Answer 2

Ответ:

Объяснение:

Пусть скорость мотоциклиста - х км/ч, тогда скорость автомобилиста

х + 20 км/ч, Время за которое проехал мотоциклист составляет 280/х ч, а автомобилиста 280/(х + 20) ч . Так как мотоциклист был в пути на 15 мин = 15/60 = 0,25 ч больше , то отсюда имеем уравнение:

280/х - 280/(х + 20) = 0,25

280 * (х + 20) - 280х = 0,25х(х + 20)

280х + 5600 - 280 х = 0,25х² + 5 х

0,25х² + 5 х - 5600 = 0  | : 0,25

х² + 20 х - 22400 = 0

D = 20² - 4 * (- 22400) = 400 + 89600 = 90000

√D = √90000 = 300

x₁ = (-20 + 300)/2 = 140 км/ч скорость мотоциклиста

х₂ = (-20 - 300)/2 = - 160 не подходит по условию задачи

Answer 3

Problem Analysis

We have two vehicles, an automobile and a motorcycle, traveling from point A to point B, with a distance of 280 km between them. The automobile travels at a speed that is 20 km/h faster than the motorcycle. We also know that the motorcycle arrives at point B 15 minutes later than the automobile. We need to determine the speed of the motorcycle.

Solution

Let's assume the speed of the motorcycle is x km/h. Since the automobile travels 20 km/h faster, its speed will be x + 20 km/h.

To find the time it takes for each vehicle to travel the distance between points A and B, we can use the formula:

Time = Distance / Speed

For the motorcycle, the time taken will be:

Time taken by motorcycle = 280 km / x km/h

For the automobile, the time taken will be:

Time taken by automobile = 280 km / (x + 20) km/h

We know that the motorcycle arrives at point B 15 minutes (or 0.25 hours) later than the automobile. So, we can set up the equation:

Time taken by motorcycle = Time taken by automobile + 0.25 hours

Substituting the values, we get:

280 / x = 280 / (x + 20) + 0.25

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

Calculation

To solve the equation, we can multiply through by the common denominator, which is x(x + 20), to eliminate the denominators:

280(x + 20) = 280x + 0.25x(x + 20)

Expanding and simplifying the equation:

280x + 5600 = 280x + 0.25x^2 + 5x

Rearranging the terms:

0.25x^2 + 5x - 5600 = 0

Now, we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 0.25, b = 5, and c = -5600. Substituting these values into the formula:

x = (-5 ± √(5^2 - 4 * 0.25 * -5600)) / (2 * 0.25)

Simplifying further:

x = (-5 ± √(25 + 5600)) / 0.5

x = (-5 ± √5625) / 0.5

x = (-5 ± 75) / 0.5

We have two possible solutions:

1. x = (-5 + 75) / 0.5 = 70 / 0.5 = 140 2. x = (-5 - 75) / 0.5 = -80 / 0.5 = -160

Since speed cannot be negative, we discard the second solution. Therefore, the speed of the motorcycle is 140 km/h.

Answer

The speed of the motorcycle is 140 km/h.