Question

Из пункта А в пункт В ,расстояние между которыми 5км,вышел пешеход .Спустя 30мин после него из того же места выехал велосипедист ,скорость которого на 10км/ч больше скорости пешехода .В пункт В велосипедист прибыл на 10 мир раньше пешехода .Найдите скорость велосипедиста и пешехода.

Answer 1

Х-скорость пешехода
х+10-велосипедиста
5/х-5/(х+10)=2/3
2х²+20х-15(х+10-х)=0
2х²+20х-150=0
х²+10х-75=0
х1+х2=-10 и х1*х2=-75
х1=-15 не удов усл
х2=5км/ч-скорость пешехода
5+10=15км/ч-скорость велосипедиста

Answer 2

Problem Analysis

We are given that a pedestrian and a cyclist start from point A and travel to point B, which are 5 km apart. The cyclist starts 30 minutes after the pedestrian and arrives at point B 10 minutes before the pedestrian. We need to find the speeds of the pedestrian and the cyclist.

Solution

Let's assume the speed of the pedestrian is x km/h. Since the cyclist's speed is 10 km/h faster than the pedestrian, the speed of the cyclist is (x + 10) km/h.

We know that the distance between point A and point B is 5 km. Let's calculate the time it takes for the pedestrian and the cyclist to travel this distance.

The time taken by the pedestrian can be calculated using the formula: time = distance / speed.

The time taken by the cyclist is the time taken by the pedestrian minus 30 minutes (0.5 hours) because the cyclist starts 30 minutes later.

The time taken by the cyclist can be calculated using the formula: time = distance / speed - 0.5.

We are given that the cyclist arrives at point B 10 minutes (0.167 hours) before the pedestrian. Therefore, the time taken by the cyclist is the time taken by the pedestrian minus 10 minutes (0.167 hours).

The equation for the time taken by the cyclist can be written as: (5 / (x + 10)) = (5 / x) - 0.167.

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

Calculation

To solve the equation (5 / (x + 10)) = (5 / x) - 0.167, we can cross-multiply and simplify:

5x = 5(x + 10) - 0.167x(x + 10).

Expanding and simplifying:

5x = 5x + 50 - 0.167x^2 - 1.67x.

Combining like terms:

0 = -0.167x^2 - 1.67x + 50.

This is a quadratic equation. Let's solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a).

For our equation, a = -0.167, b = -1.67, and c = 50.

Substituting the values into the quadratic formula:

x = (-(-1.67) ± √((-1.67)^2 - 4(-0.167)(50))) / (2(-0.167)).

Simplifying:

x = (1.67 ± √(2.7889 + 33.4)) / (-0.334).

x = (1.67 ± √36.1889) / (-0.334).

Taking the square root:

x = (1.67 ± 6.016) / (-0.334).

Calculating the two possible values of x:

x1 = (1.67 + 6.016) / (-0.334) ≈ -21.96.

x2 = (1.67 - 6.016) / (-0.334) ≈ 16.56.

Since speed cannot be negative, the speed of the pedestrian is approximately 16.56 km/h.

The speed of the cyclist is 10 km/h faster, so the speed of the cyclist is approximately 26.56 km/h.

Answer

The speed of the pedestrian is approximately 16.56 km/h, and the speed of the cyclist is approximately 26.56 km/h.