Question

5. Два велосипедиста, находясь друг от друга на расстоянии 9 км, выехали одновременно навстречу друг другу и через 20 мин встретились. Когда же они выехали из одного пункта в одном направлении, то через 1ч 40 мин один отстал от другого на 5 км. Какова скорость каждого велосипедиста?

Answer 1

S = v * t - формула пути
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S = 5 км - расстояние; t = 1 ч 40 мин = 1 40/60 = 1 2/3 ч - время в пути
v = 5 : 1 2/3 = 5 : 5/3 = 5 * 3/5 = 3 (км/ч) - скорость отставания (на столько меньше скорость одного из велосипедистов)

S = 9 км - расстояние; t = 20 мин = 20/60 = 1/3 ч - время в пути
Пусть х (км/ч) - скорость одного велосипедиста, тогда х + 3 (км/ч) - скорость другого велосипедиста, v = х + х + 3 = 2х + 3 (км/ч) - скорость сближения. Уравнение:
(2х + 3) * 1/3 = 9
2/3х + 1 = 9
2/3х = 9 - 1
2/3х = 8
х = 8 : 2/3 = 8 * 3/2 = 4 * 3
х = 12 (км/ч) - скорость одного велосипедиста
12 + 3 = 15 (км/ч) - скорость другого велосипедиста
Ответ: 12 км/ч и 15 км/ч.

Проверка: 
(15 - 12) * 1 2/3 = 3 * 5/3 = 5
(15 + 12) * 1/3 = 27/3 = 9

Answer 2

Problem Analysis

We have two cyclists who start at a distance of 9 km from each other and ride towards each other. After 20 minutes, they meet. Later, when they start from the same point in the same direction, one cyclist is 5 km ahead of the other after 1 hour and 40 minutes. We need to find the speed of each cyclist.

Solution

Let's assume the speed of the first cyclist is x km/h and the speed of the second cyclist is y km/h.

When the cyclists are riding towards each other, their relative speed is the sum of their individual speeds. So, the relative speed is x + y km/h.

Given that they meet after 20 minutes, which is 1/3 of an hour, we can write the equation:

Distance = Speed × Time

For the first cyclist, the distance covered is x × (1/3) km.

For the second cyclist, the distance covered is y × (1/3) km.

Since they meet, the sum of their distances covered should be equal to the total distance between them, which is 9 km. Therefore, we have the equation:

(x × (1/3)) + (y × (1/3)) = 9 ---(Equation 1)

Now, let's consider the scenario where they start from the same point in the same direction. In this case, the relative speed is the difference between their individual speeds. So, the relative speed is x - y km/h.

Given that one cyclist is 5 km ahead of the other after 1 hour and 40 minutes, which is 1.67 hours, we can write the equation:

Distance = Speed × Time

For the first cyclist, the distance covered is x × 1.67 km.

For the second cyclist, the distance covered is y × 1.67 km.

Since one cyclist is 5 km ahead of the other, we have the equation:

(x × 1.67) - (y × 1.67) = 5 ---(Equation 2)

We now have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system of equations to find the values of x and y.

Solving the Equations

Let's solve the system of equations (Equation 1 and Equation 2) to find the values of x and y.

From Equation 1, we have:

(x × (1/3)) + (y × (1/3)) = 9

Multiplying both sides of the equation by 3 to eliminate the fractions, we get:

x + y = 27 ---(Equation 3)

From Equation 2, we have:

(x × 1.67) - (y × 1.67) = 5

Dividing both sides of the equation by 1.67, we get:

x - y = 3 ---(Equation 4)

Now, we have a system of two equations (Equation 3 and Equation 4) with two variables (x and y). We can solve this system of equations to find the values of x and y.

Adding Equation 3 and Equation 4, we get:

(x + y) + (x - y) = 27 + 3

Simplifying the equation, we get:

2x = 30

Dividing both sides of the equation by 2, we get:

x = 15

Substituting the value of x into Equation 3, we get:

15 + y = 27

Simplifying the equation, we get:

y = 12

Therefore, the speed of the first cyclist is 15 km/h and the speed of the second cyclist is 12 km/h.

Answer

The speed of the first cyclist is 15 km/h and the speed of the second cyclist is 12 km/h.