Question

С решением пожалуйста!В зале кинотеатра имеются две двери. После сеанса зрители выходят через обе двери в течение трех минут. Если их выпускать через одну большую дверь, то выход из зала займет времени на 2.1/2 мин меньше, чем в том случае, если их выпускать через меньшую дверь. Сколько времени требуется для выпуска зрителей из зала кино через каждую дверь в отдельности?

Answer 1

Х- время выхода через большую дверь
х+2,5 мин-время выхода через малую дверь

1/х+1/(х+2,5)=1/3
1/х+1/(х+2,5)-1/3=0 домножим на х(х+2,5)
(х+2,5)+х-1/3х(х+2,5)=0
2х+2,5-1/3х²-2,5/3х=0 домножим на 3
6х+7,5-х²-2,5х=0
-х²+3,5х+7,5=0
х²-3,5х-7,5=0
D = (-3.5)2 - 4·1·(-7.5) = 12.25 + 30 = 42.25
х₁=-1,5 не подходит
х₂=5 мин- - время выхода через большую дверь
5+2,5=7,5 мин-- время выхода через  малую дверь

Answer 2

Problem Analysis

In the cinema hall, there are two doors through which the audience exits after a movie. If they are released through one large door, it takes 2.5 minutes less than if they are released through the smaller door. We need to determine the time required to release the audience through each door separately.

Solution

Let's assume that the time required to release the audience through the smaller door is x minutes. According to the given information, the time required to release the audience through the larger door is x - 2.5 minutes.

We know that the total time required to release the audience through both doors is 3 minutes. Therefore, we can set up the following equation:

x + (x - 2.5) = 3

Simplifying the equation, we get:

2x - 2.5 = 3

Adding 2.5 to both sides of the equation, we get:

2x = 5.5

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

x = 2.75

Therefore, the time required to release the audience through the smaller door is 2.75 minutes.

To find the time required to release the audience through the larger door, we subtract 2.5 minutes from the time required for the smaller door:

2.75 - 2.5 = 0.25

Therefore, the time required to release the audience through the larger door is 0.25 minutes.

Answer

The time required to release the audience through the smaller door is 2.75 minutes, and the time required to release the audience through the larger door is 0.25 minutes.