Question

Из пункта А в пункт Б расстояние между которыми 50 км,одновременно выехали автомобилист и велосипедист.Известно,что в час автомобилист проезжает на 40км больше,чем велосипедист.Определите скорость велосипедиста,если известно,что он прибыл в пункт Б на 1ч 40мин позже автомобилиста.Ответ в км/ч

Answer 1

     Zsedinaглавный мозг ответила 12.04.2014 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 the distance between point A and point B is 50 km. An automobile driver and a cyclist simultaneously start their journey from point A to point B. It is known that the automobile driver travels 40 km more per hour than the cyclist. We need to determine the speed of the cyclist if we know that the cyclist arrives at point B 1 hour and 40 minutes later than the automobile driver.

Solution

Let's assume the speed of the cyclist is x km/h. Since the automobile driver travels 40 km more per hour than the cyclist, the speed of the automobile driver is x + 40 km/h.

We can use the formula distance = speed × time to calculate the time taken by each traveler.

The time taken by the cyclist to travel from point A to point B is given by: time taken by cyclist = distance / speed of cyclist = 50 / x hours.

The time taken by the automobile driver to travel from point A to point B is given by: time taken by automobile driver = distance / speed of automobile driver = 50 / (x + 40) hours.

We are given that the cyclist arrives at point B 1 hour and 40 minutes later than the automobile driver. Converting 1 hour and 40 minutes to hours, we get: 1 hour and 40 minutes = 1 + 40/60 = 1.67 hours.

According to the given information, the time taken by the cyclist is 1.67 hours more than the time taken by the automobile driver. Therefore, we can set up the following equation:

50 / x = 50 / (x + 40) + 1.67

To solve this equation, we can multiply both sides by x(x + 40) to eliminate the denominators:

50(x + 40) = 50x + 1.67x(x + 40)

Simplifying the equation:

50x + 2000 = 50x + 1.67x^2 + 67.68x

Combining like terms:

1.67x^2 + 67.68x - 2000 = 0

Now we have a quadratic equation. We can solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, the values of a, b, and c are:

a = 1.67 b = 67.68 c = -2000

Substituting these values into the quadratic formula:

x = (-67.68 ± √(67.68^2 - 4 * 1.67 * -2000)) / (2 * 1.67)

Simplifying further:

x = (-67.68 ± √(4572.9024 + 13360)) / 3.34

x = (-67.68 ± √(17932.9024)) / 3.34

x = (-67.68 ± 133.8) / 3.34

Now we have two possible values for x. Let's calculate them:

x1 = (-67.68 + 133.8) / 3.34 = 66.12 / 3.34 ≈ 19.82

x2 = (-67.68 - 133.8) / 3.34 = -201.48 / 3.34 ≈ -60.36

Since speed cannot be negative, we discard the negative value of x. Therefore, the speed of the cyclist is approximately 19.82 km/h.

Answer

The speed of the cyclist is approximately 19.82 km/h.