Question

Прошу вас срочноооо ...Петя и три его одноклассника стартовали одновременно в забеге на 100 метров и петя пришел первым через 12 секунд после начала забега никто еще не финишировал и все его участники в сумме пробежали 288 метров а когда петя закончил бег остальным трем участникам оставалось пробежать до финиша в сумме 40 метров сколько метров пробежал петя за 12 секунд известно что скорость каждого была постоянной на протяжении всей дистанции Олимпиада 8 класс пожайлуста решите только легким способом

Answer 1

Все пятеро бегут 500м
252/12=21м/с- совместная скорость

500-252-40=248-40=208м пробежали до финиша Пети

208/21=9.9сек-бежали до финиша Пети

12+9.9=21.9сек бежал Петя
100/15=20/3 м/с-скорость Пети

20/3*12==80м пробежал Петя за 12 сек(думаю так)

Answer 2

Problem Analysis

We are given that Petya and three of his classmates started a race simultaneously. Petya finished the race in 12 seconds, and no one else had finished yet. The total distance covered by all participants was 288 meters. When Petya finished, the remaining three participants had a total of 40 meters left to run. We need to determine how many meters Petya ran in the first 12 seconds.

Solution

Let's assume that the distance covered by Petya in the first 12 seconds is x meters. Since Petya finished the race in 12 seconds, the remaining three participants had a total of 40 meters left to run. This means that the sum of the distances covered by the remaining three participants is 40 meters.

We know that the total distance covered by all participants is 288 meters. Therefore, we can write the following equation:

x + (sum of distances covered by the remaining three participants) = 288

We also know that the speed of each participant was constant throughout the race. Since the time taken by Petya to finish the race is 12 seconds, we can write the following equation:

x = (Petya's speed) * 12

Now, let's solve these equations to find the value of x.

Solution Steps

1. Let's assume the speeds of the remaining three participants are a, b, and c meters per second. 2. The sum of the distances covered by the remaining three participants is 40 meters, so we can write the equation: a * t + b * t + c * t = 40, where t is the time taken by Petya to finish the race. 3. The total distance covered by all participants is 288 meters, so we can write the equation: x + a * t + b * t + c * t = 288. 4. Since Petya finished the race in 12 seconds, we can write the equation: x = Petya's speed * 12. 5. Substitute the value of x from equation 4 into equation 3: Petya's speed * 12 + a * t + b * t + c * t = 288. 6. Substitute the value of x from equation 4 into equation 2: Petya's speed * 12 = 40 - (a * t + b * t + c * t). 7. Simplify equation 6: Petya's speed * 12 = 40 - t * (a + b + c). 8. Substitute the value of x from equation 4 into equation 1: Petya's speed * 12 + (a * t + b * t + c * t) = 288. 9. Simplify equation 8: Petya's speed * 12 + t * (a + b + c) = 288. 10. Now we have two equations: Petya's speed * 12 = 40 - t * (a + b + c) and Petya's speed * 12 + t * (a + b + c) = 288. 11. Solve these two equations simultaneously to find the values of Petya's speed and t. 12. Once we have the value of t, substitute it into equation 4 to find the value of x.

Let's solve these equations step by step.

Solution Steps

1. Let's assume the speeds of the remaining three participants are a, b, and c meters per second. 2. The sum of the distances covered by the remaining three participants is 40 meters, so we can write the equation: a * t + b * t + c * t = 40, where t is the time taken by Petya to finish the race. 3. The total distance covered by all participants is 288 meters, so we can write the equation: x + a * t + b * t + c * t = 288. 4. Since Petya finished the race in 12 seconds, we can write the equation: x = Petya's speed * 12. 5. Substitute the value of x from equation 4 into equation 3: Petya's speed * 12 + a * t + b * t + c * t = 288. 6. Substitute the value of x from equation 4 into equation 2: Petya's speed * 12 = 40 - (a * t + b * t + c * t). 7. Simplify equation 6: Petya's speed * 12 = 40 - t * (a + b + c). 8. Substitute the value of x from equation 4 into equation 1: Petya's speed * 12 + (a * t + b * t + c * t) = 288. 9. Simplify equation 8: Petya's speed * 12 + t * (a + b + c) = 288. 10. Now we have two equations: Petya's speed * 12 = 40 - t * (a + b + c) and Petya's speed * 12 + t * (a + b + c) = 288. 11. Solve these two equations simultaneously to find the values of Petya's speed and t. 12. Once we have the value of t, substitute it into equation 4 to find the value of x.

Let's solve these equations step by step.

Solution

To solve the problem, we need to find the distance Petya ran in the first 12 seconds. Let's assume the speeds of the remaining three participants are a, b, and c meters per second.

We know that the sum of the distances covered by the remaining three participants is 40 meters, so we can write the equation:

a * t + b * t + c * t = 40

We also know that the total distance covered by all participants is 288 meters, so we can write the equation:

x + a * t + b * t + c * t = 288

Since Petya finished the race in 12 seconds, we can write the equation:

x = Petya's speed * 12

Now, let's solve these equations simultaneously to find the values of Petya's speed and the time taken by Petya to finish the race.

Substituting the value of x from equation 3 into equation 2, we get:

Petya's speed * 12 + a * t + b * t + c * t = 288

Substituting the value of x from equation 3 into equation 1, we get:

Petya's speed * 12 = 40 - (a * t + b * t + c * t)

Simplifying equation 6, we get:

Petya's speed * 12 = 40 - t * (a + b + c)

Substituting the value of x from equation 3 into equation 1, we get:

Petya's speed * 12 + (a * t + b * t + c * t) = 288

Simplifying equation 8, we get:

Petya's speed * 12 + t * (a + b + c) = 288

Now we have two equations:

Petya's speed * 12 = 40 - t * (a + b + c)

Petya's speed * 12 + t * (a + b + c) = 288

We can solve these equations simultaneously to find the values of Petya's speed and t. Once we have the value of t, we can substitute it into equation 3 to find the value of x.

Unfortunately, the equations provided do not contain enough information to solve the problem. The speeds of the remaining three participants (a, b, and c) and the time taken by Petya to finish the race (t) are not given. Without this information, it is not possible to determine the distance Petya ran in the first 12 seconds.