Question

Ванна объёмом 100 л. снабжена краном и сливом , находящимся под краном . Из открытого крана в ванну каждую минуту вливается 2 литра воды. Открытый слив пропускает 3 литра воды в минуту . Сначала кран и слив были закрыты , а ванна пуста. В 12 .00 открыли кран. В 12.30 открыли слив. В 14. 00 закрыли слив. В какой момент ванна наполнилась целиком?

Answer 1

Несколько ящиков вместе весят 10 тонн причем каждый из них весит неболее одной тонны.Сколько трехтонок заведомо достаточно чтоб увезти этот груз

Answer 2

Problem Analysis

We are given a bathtub with a capacity of 100 liters. The bathtub has a faucet and a drain. The faucet pours 2 liters of water into the bathtub every minute, while the drain lets out 3 liters of water per minute. The faucet and drain were initially closed, and the bathtub was empty. We need to determine at what point the bathtub is completely filled.

Solution

To solve this problem, we need to keep track of the amount of water in the bathtub at different time intervals.

Let's break down the timeline of events: - At 12:00, the faucet is opened and starts pouring water into the bathtub. - At 12:30, the drain is opened and starts letting water out of the bathtub. - At 14:00, the drain is closed.

To find the moment when the bathtub is completely filled, we need to calculate the net amount of water added to the bathtub during this time.

Calculation

Let's calculate the net amount of water added to the bathtub during the given time intervals.

From 12:00 to 12:30 (30 minutes): - The faucet pours 2 liters of water per minute. - Therefore, in 30 minutes, the faucet adds 2 liters/minute * 30 minutes = 60 liters of water to the bathtub.

From 12:30 to 14:00 (90 minutes): - The faucet pours 2 liters of water per minute. - The drain lets out 3 liters of water per minute. - Therefore, the net amount of water added to the bathtub during this time is 2 liters/minute - 3 liters/minute = -1 liter/minute. - In 90 minutes, the net amount of water added is -1 liter/minute * 90 minutes = -90 liters.

Adding the net amounts of water added during the two time intervals: - 60 liters + (-90 liters) = -30 liters.

Since the net amount of water added is negative (-30 liters), the bathtub will not be completely filled. Therefore, the bathtub does not fill up completely during the given time intervals.

Answer

The bathtub does not fill up completely during the given time intervals.

Note: The calculation assumes that the faucet and drain operate continuously at a constant rate throughout the given time intervals.