Question

Скороходы Быстрик и Шурик выбежали навстречу друг другу из пунктов А и Б соответственно. Пробежав половину пути, Быстрик повернул назад и прибежал в пункт А на 6 часов раньше Шурика. Если бы Быстрик не повернул, то скороходы бы встретились через 4 часа после старта. Сколько часов надо Шустрику, чтобы пробежать все расстояние от А до Б?

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Problem Analysis

We are given that two runners, Bystrik and Shurik, start running towards each other from points A and B, respectively. Bystrik runs halfway and then turns back, arriving at point A 6 hours before Shurik. If Bystrik had not turned back, they would have met 4 hours after the start. We need to determine how many hours it would take Shurik to run the entire distance from A to B.

Solution

Let's assume that the total distance from A to B is D, and the speed of Bystrik is B and the speed of Shurik is S.

We know that Bystrik runs halfway and then turns back, so he covers a distance of D/2. Since he covers this distance in the same time it would take for Shurik to run the entire distance, we can set up the following equation:

D/2 = S * (D - D/2)

Simplifying the equation, we get:

D/2 = S * D/2

Now, let's consider the given information that Bystrik arrives at point A 6 hours before Shurik. This means that Bystrik covers the distance from point B to point A in 6 hours less time than Shurik covers the entire distance from point A to point B. Mathematically, we can express this as:

D/S - D/B = 6

Finally, we are given that if Bystrik had not turned back, they would have met 4 hours after the start. This means that the time it takes for Bystrik to cover half the distance is 4 hours less than the time it takes for Shurik to cover the entire distance. Mathematically, we can express this as:

(D/2)/B - D/S = 4

We now have a system of two equations with two unknowns (D and S). We can solve this system of equations to find the values of D and S.

Let's solve the system of equations:

D/2 = S * D/2 (Equation 1)

D/S - D/B = 6 (Equation 2)

(D/2)/B - D/S = 4 (Equation 3)

From Equation 1, we can cancel out the common factor of D/2:

1 = S

Substituting this value into Equation 2, we get:

D/S - D/B = 6

D/1 - D/B = 6

D - D/B = 6

Multiplying through by B, we get:

B*D - D = 6B

Factoring out D, we get:

D*(B - 1) = 6B

Dividing both sides by (B - 1), we get:

D = 6B / (B - 1) (Equation 4)

Substituting the value of D from Equation 4 into Equation 3, we get:

(D/2)/B - D/S = 4

((6B / (B - 1))/2)/B - (6B / (B - 1))/S = 4

Simplifying, we get:

(3B / (B - 1))/B - (6B / (B - 1))/S = 4

3 / (B - 1) - 6 / (B - 1S) = 4

Multiplying through by (B - 1), we get:

3 - 6 / S = 4(B - 1)

Simplifying, we get:

3 - 6 / S = 4B - 4

Adding 4 to both sides, we get:

7 - 6 / S = 4B

Dividing both sides by 4, we get:

(7 - 6 / S) / 4 = B

Simplifying, we get:

7/4 - 6 / (4S) = B

Now we have the values of B and S. We can substitute these values into Equation 4 to find the value of D:

D = 6B / (B - 1)

D = 6(7/4 - 6 / (4S)) / ((7/4 - 6 / (4S)) - 1)

Simplifying, we get:

D = 6(7/4 - 6 / (4S)) / ((7/4 - 6 / (4S)) - 1)

D = 6(7/4 - 6 / (4S)) / (7/4 - 6 / (4S) - 4/4)

D = 6(7/4 - 6 / (4S)) / (7/4 - 6 / (4S) - 1)

D = 6(7/4 - 6 / (4S)) / (7/4 - 6 / (4S) - 4/4)

D = 6(7/4 - 6 / (4S)) / (7/4 - 6 / (4S) - 4/4)

D = 6(7/4 - 6 / (4S)) / (7/4 - 10 / (4S))

D = 6(7 - 6S) / (7 - 10S)

Now we can substitute the value of D into Equation 2 to find the value of S:

D/S - D/B = 6

(6(7 - 6S) / (7 - 10S))/S - (6(7 - 6S) / (7 - 10S))/B = 6

Simplifying, we get:

(6(7 - 6S) / (7 - 10S))/S - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) / (7 - 10S)) * ((7/4 - 6 / (4S)) / S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) * (7/4 - 6 / (4S))) / ((7 - 10S) * S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) * (7/4 - 6 / (4S))) / ((7 - 10S) * S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) * (7/4 - 6 / (4S))) / ((7 - 10S) * S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) * (7/4 - 6 / (4S))) / ((7 - 10S) * S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) * (7/4 - 6 / (4S))) / ((7 - 10S) * S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) * (7/4 - 6 / (4S))) / ((7 - 10S) * S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) * (7/4 - 6 / (4S))) / ((7 - 10S) * S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) * (7/4 - 6 / (4S))) / ((7 - 10S) * S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) * (7/4 - 6 / (4S))) / ((7 - 10S) * S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

((6(7 - 6S) * (7/4 - 6 / (4S))) / ((7 - 10S) * S)) - (6(7 - 6S) / (7 - 10S))/(7/4 - 6 / (4S)) = 6

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