Question

Из пункта А в пункт В, расстояние между которыми 50 км, одновременно выехали автомобилист и велосипедист. Известно, что в час автомобилист проезжает на 60 км больше, чем велосипедист. Определите скорость велосипедиста, если известно, что он прибыл в пункт В на 2 часа 40 минут позже автомобилиста. Ответ дайте в км/ч

Answer 1

S -50км
Vвелосипедиста -х
Vавтомоболиста-х+80
 2ч 40мин- 8/3 часа
нам формула известна  t = S / V
30 /x - 30 / (x+80) = 8/3
30х + 2400 -30х = 8/3 *х(х+80)
x2 +80x - 900=0 
x1=10
x2= -90.
и всё нам теперь время известно 10ч

Answer 2

Скорость велосипедиста х , автомобилиста х+50 
60/х -60/(х+50)=5 
(60*(х+50)-60*х-5х*(х+50))/(х*(х+50))=0 х не может быть равен0, -50 
60x+3000-60x-5x^-250x=0 
-5x^-250x+3000=0 
x^+50x-600=0 
D=2500-4*(-600)=70^ 
x1=(-50-70)/2=-60 не отвечает условию задачи 
х2=(-50+70)/2=10 
Ответ 10 км/ч

Answer 3

Problem Analysis

We are given that a car and a cyclist simultaneously left point A and traveled towards point B, which are 50 km apart. The car travels 60 km/h faster than the cyclist. We need to determine the speed of the cyclist if we know that the cyclist arrived at point B 2 hours and 40 minutes later than the car.

Solution

Let's assume the speed of the cyclist is x km/h. Since the car travels 60 km/h faster than the cyclist, the speed of the car is x + 60 km/h.

We can use the formula distance = speed × time to calculate the time taken by each of them to travel from point A to point B.

The time taken by the cyclist is given by: time taken by cyclist = distance / speed of cyclist

The time taken by the car is given by: time taken by car = distance / speed of car

We know that the time taken by the cyclist is 2 hours and 40 minutes (or 2.67 hours) more than the time taken by the car. So we can write the equation:

time taken by cyclist = time taken by car + 2.67

Substituting the formulas for time taken by each of them, we get:

distance / speed of cyclist = distance / speed of car + 2.67

Since the distance is the same for both, we can cancel it out:

1 / speed of cyclist = 1 / speed of car + 2.67

Now we can substitute the values of the speed of the cyclist and the car:

1 / x = 1 / (x + 60) + 2.67

To solve this equation, we can multiply both sides by x(x + 60) to eliminate the fractions:

x(x + 60) / x = x(x + 60) / (x + 60) + 2.67(x + 60)

Simplifying the equation:

x + 60 = x(x + 60) + 2.67(x + 60)

Expanding and simplifying further:

x + 60 = x^2 + 60x + 2.67x + 160.2

Rearranging the equation:

x^2 + 23.67x - 100.2 = 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 = 1, b = 23.67, and c = -100.2.

Solving the equation, we get two possible solutions for x. We will consider the positive value since speed cannot be negative:

x = 3.3 (rounded to one decimal place)

Therefore, the speed of the cyclist is 3.3 km/h.

Answer

The speed of the cyclist is 3.3 km/h.