Question

Петя и Вася пошли на день рождения к своему другу Толе. Толя звал их на 12:00, но друзья перепутали. Петя пришёл, когда до двух часов дня оставалось вдвое меньше, чем прошло после полудня. А Вася – когда до двух часов дня оставалось вдвое больше, чем прошло после 13:00. Кто пришёл раньше?помоготи срочна поставлю 35 баллов

Answer 1

Ответ:

Петя и Вася пришли одновременно

Пошаговое объяснение:

Пусть Петя пришел в "х" часов. Тогда после полудня прошло х - 12 часов, а до двух часов дня (14 часов) осталось 14 - х часов, что вдвое меньше.

уравнение: х - 12 = (14 - х)*2

х - 12 = 28 - 2х

х + 2х = 28 + 12

3х = 40

х = 40/3=13 1/3 то есть Петя пришел в 13:20.

Пусть Вася пришел в "у" часов. Тогда после 13:00 прошло у - 13 часов, а до двух часов дня (14 часов) осталось 14 - у часов, что вдвое больше.

14 - у = (у - 13) *2

14 - у = 2у - 26

3у = 40

у=40/3 = 13 1/3 то есть Вася тоже пришел в 13:20.

Answer 2

Who arrived earlier, Petya or Vasya?

To determine who arrived earlier, let's analyze the information provided.

According to the information given, Petya arrived when there was twice as much time left until 2:00 PM as had passed after noon. On the other hand, Vasya arrived when there was twice as much time left until 2:00 PM as had passed after 1:00 PM.

To solve this problem, we can set up equations based on the information given.

Let's assume that x represents the time that has passed after noon until Petya arrived, and y represents the time that has passed after 1:00 PM until Vasya arrived.

From the information given, we can set up the following equations:

Equation 1: x = 2(2 - x/60) Equation 2: y = 2(2 - y/60)

Simplifying these equations, we get:

Equation 1: x = 4 - x/30 Equation 2: y = 4 - y/30

To solve these equations, we can multiply both sides of each equation by 30 to eliminate the fractions:

Equation 1: 30x = 120 - x Equation 2: 30y = 120 - y

Simplifying further:

Equation 1: 31x = 120 Equation 2: 31y = 120

Solving for x and y:

x = 120/31 y = 120/31

Since x and y are equal, it means that Petya and Vasya arrived at the same time.

Therefore, neither Petya nor Vasya arrived earlier. They both arrived at the same time.

Please let me know if I can help you with anything else.