Question

Из пункта А в пункт Б, расстояние между которыми 50 километров, одновременно выехали автомобилист и велосипедист. Известно, что в час автомобилист проезжает на 65 километров больше, чем велосипедист. Определите скорость велосипедиста если, известно, что он прибыл в пункт Б на 4 часа 20 минут позже автомобилиста

Answer 1

Х-скорость велосипедиста,50/х-время
х+80-скорость автомобилиста,50/(х+80)-время
50/х-80/(х+80)=2
50*(х+80)-50*х=2х*(х+80)
50(х+80-х)=2х²+160х
2х²+160х-4000=0
х²+80х-2000=0
х1+х2=-80 и х1*х2=-2000⇒х1=20 и х2=-100-не удов. усл.
Ответ : скорость велосипедиста 20км/ч

Answer 2

Problem Analysis

We are given that a car and a cyclist simultaneously left point A and are traveling towards point B, which is 50 kilometers away. It is known that the car travels 65 kilometers more per hour than the cyclist. We need to determine the speed of the cyclist if we know that the cyclist arrived at point B 4 hours and 20 minutes later than the car.

Solution

Let's assume the speed of the cyclist is x kilometers per hour. Since the car travels 65 kilometers more per hour than the cyclist, the speed of the car is x + 65 kilometers per hour.

To find the time it takes for each to reach point B, we can use the formula time = distance / speed.

The time taken by the cyclist to reach point B is given as 4 hours and 20 minutes, which is equivalent to 4.33 hours.

The time taken by the car to reach point B is the same as the time taken by the cyclist plus 4 hours and 20 minutes.

We can set up the following equation to solve for the speed of the cyclist:

50 / x = (50 / (x + 65)) + 4.33

Let's solve this equation to find the speed of the cyclist.

Calculation

Using the equation 50 / x = (50 / (x + 65)) + 4.33, we can solve for x.

Simplifying the equation, we get:

50 / x - 50 / (x + 65) = 4.33

To solve this equation, we can multiply both sides by x(x + 65) to eliminate the denominators:

50(x + 65) - 50x = 4.33x(x + 65)

Simplifying further:

50x + 3250 - 50x = 4.33x^2 + 281.45x

Combining like terms:

3250 = 4.33x^2 + 281.45x

Rearranging the equation:

4.33x^2 + 281.45x - 3250 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c into the quadratic formula:

x = (-281.45 ± √(281.45^2 - 4 * 4.33 * -3250)) / (2 * 4.33)

Calculating the values inside the square root:

x = (-281.45 ± √(79184.9025 + 56290)) / 8.66

x = (-281.45 ± √(135474.9025)) / 8.66

x = (-281.45 ± 367.97) / 8.66

Simplifying further:

x = (-649.42) / 8.66 or x = 86.52 / 8.66

Calculating the values:

x = -74.99 or x = 10

Since speed cannot be negative, the speed of the cyclist is 10 kilometers per hour.

Answer

The speed of the cyclist is 10 kilometers per hour.