Question

Решите пожалуйста. из одного пункта в одном направлении каждые пол часа выезжает велосипедист. Первый едет со скоростью 10 км/ч, а второй 8 км/ч. Найдите скорость третьего, если известно, что он догнал первого велосипедиста на 4 часа позже, чем второго.

Answer 1

Пусть скорость третьего равна v км в час

(v-8) км в час - скорость сближения третьего со вторым

Второй выехал на полчаса раньше третьего и проехал за эти полчаса 4 км

$\frac{4}{v-8}$  час - время, за которое третий догонит второго

(v-10) км в час - скорость сближения третьего со вторым

Первый выехал на час раньше третьего и проехал за этот час 10 км

$\frac{10}{v-10}$  час - время, за которое третий догонит второго

Уравнение:

$\frac{10}{v-10} =\frac{4}{v-8}+4$

$\frac{10}{v-10} =\frac{4+4(v-8)}{v-8}\\\\\frac{10}{v-10} =\frac{4+4v-32)}{v-8}\\\\\frac{10}{v-10} =\frac{4v-28}{v-8}\\\\10(v-8)=(4v-28)(v-10)$;   $v\neq 8; v\neq 10$

$10(v-8)=2(2v-14)(v-10)$

$5v-40=2v^2-14v-20v+140\\\\2v^2-39v+180=0$

D=(-39)²-4·2·180=81

$v_{1}=\frac{39-9}{4}=7,5$   или  $v_{2}=\frac{39+9}{4}=12$

$v_{1}=7,5 < 8;\\\\v_{1}=7,5 < 10$

С такой скоростью третий не догонит ни второго, ни первого

О т в е т. 12 км в час

Answer 2

Ответ:

12 км/ч

Объяснение:

Answer 3

Problem Analysis

We are given that two cyclists start from the same point in the same direction every half hour. The first cyclist has a speed of 10 km/h, and the second cyclist has a speed of 8 km/h. We need to find the speed of the third cyclist, given that they catch up to the first cyclist 4 hours after the second cyclist.

Solution

Let's assume that the third cyclist has a speed of v km/h.

To solve this problem, we can use the concept of relative speed. The relative speed between two objects moving in the same direction is the difference between their individual speeds.

Let's consider the time it takes for the third cyclist to catch up to the first cyclist. Since the first cyclist has a head start of 4 hours, the time taken by the third cyclist to catch up to the first cyclist is the same as the time taken by the second cyclist to catch up to the first cyclist.

Let's calculate the time taken by the second cyclist to catch up to the first cyclist. We can use the formula:

Time = Distance / Speed

The distance covered by the second cyclist is the same as the distance covered by the first cyclist during this time. Since both cyclists travel at a constant speed, the distance covered is equal to the product of their speeds and the time taken.

Let's calculate the time taken by the second cyclist to catch up to the first cyclist:

Time taken by the second cyclist = Distance / Speed of the second cyclist

Time taken by the second cyclist = Distance / 8

Now, let's calculate the distance covered by the second cyclist:

Distance covered by the second cyclist = Speed of the second cyclist * Time taken by the second cyclist

Distance covered by the second cyclist = 8 * (Time taken by the second cyclist)

Since the third cyclist catches up to the first cyclist at the same time as the second cyclist, the distance covered by the third cyclist is the same as the distance covered by the second cyclist.

Distance covered by the third cyclist = Distance covered by the second cyclist

Distance covered by the third cyclist = 8 * (Time taken by the second cyclist)

Now, let's calculate the time taken by the third cyclist to catch up to the first cyclist:

Time taken by the third cyclist = Distance covered by the third cyclist / Speed of the third cyclist

Time taken by the third cyclist = (8 * (Time taken by the second cyclist)) / v

Since the time taken by the third cyclist to catch up to the first cyclist is 4 hours more than the time taken by the second cyclist, we can set up the following equation:

(8 * (Time taken by the second cyclist)) / v = Time taken by the second cyclist + 4

Now, let's solve this equation to find the value of v.

(8 * (Time taken by the second cyclist)) / v = Time taken by the second cyclist + 4

(8 * (Distance covered by the second cyclist) / 8) / v = (Distance covered by the second cyclist / 8) + 4

(Distance covered by the second cyclist) / v = (Distance covered by the second cyclist / 8) + 4

1 / v = 1 / 8 + 4

1 / v = 1 / 8 + 32 / 8

1 / v = 33 / 8

v = 8 / 33

Therefore, the speed of the third cyclist is 8 / 33 km/h.

Answer

The speed of the third cyclist is 8 / 33 km/h.