Question

Два крана,включенные одновременно,заполняют бак за 12 минут. Если бы первый кран работал один,то на заполнение бака ему понадобилось бы 18 минут. Сколько минут на это потребуется второму крану ? Подробно

Answer 1

1/12часть - бака за 1 мин заполняют оба крана

1/18 часть бака за 1 мин - заполняет І кран

1/12 - 1/18=1/36 (часть) - за 1 мин. заполняет ІІ кран.

Чтобы заполнить весь бак,ІІ крану понадобится 36минут.

Answer 2

Problem Analysis

We are given that two taps, when turned on simultaneously, can fill a tank in 12 minutes. If the first tap were to work alone, it would take 18 minutes to fill the tank. We need to determine how long it would take for the second tap to fill the tank on its own.

Solution

Let's assume that the first tap can fill 1 unit of the tank's capacity per minute. Therefore, in 12 minutes, the first tap can fill 12 units of the tank's capacity. Similarly, if the first tap were to work alone, it would take 18 minutes to fill 18 units of the tank's capacity.

Now, let's assume that the second tap can fill x units of the tank's capacity per minute. Therefore, in 12 minutes, the second tap can fill 12x units of the tank's capacity. Since the combined filling rate of both taps is equal to the filling rate of the first tap alone, we can set up the following equation:

12 + 12x = 18

Simplifying the equation, we get:

12x = 6

Dividing both sides of the equation by 12, we find:

x = 0.5

Therefore, the second tap can fill 0.5 units of the tank's capacity per minute.

To determine how long it would take for the second tap to fill the tank on its own, we need to find the reciprocal of its filling rate. The reciprocal of 0.5 is 2. Therefore, it would take the second tap 2 minutes to fill the tank on its own.

Answer

The second tap would take 2 minutes to fill the tank on its own.

Explanation

When both taps are turned on simultaneously, they can fill the tank in 12 minutes. If the first tap were to work alone, it would take 18 minutes to fill the tank. By setting up an equation and solving for the filling rate of the second tap, we find that it can fill 0.5 units of the tank's capacity per minute. Therefore, it would take the second tap 2 minutes to fill the tank on its own