Question

Один насос может выкачать всю воду из катлована за 36 ч а другой в 2 раза быстрее .после того как они работая вместе выкачали 1/3 всей воды , второй насос сломался , и остальную воду выкачал оди н первый насос .за сколько времени была выкачана вся вода из этого котлована?

Answer 1

Легко же :)


пусть вся вода в котловане-1

1:36=1/36 воды в час выкачивает первый насос

36:2=18 часов требуется второму насосу, чтобы выкочать всю воду из котлована

1:18=1/18 воды в час выкачивает второй насос

1/36+1/18=1/36+2/36=3/36=1/12 воды в час выкачивыют два насоса вместе

1:1/12=1*12/1=12 часов требуется двум насосам для выкачивания всей воды (это действие необязательно)

1/3:1/12=1/3*12/1=12/3=4 часа качали 1/3 воды оба насоса

1-1/3=3/3-1/3=2/3 воды осталось выкачать

2/3:1/36=2/3*36/1=72/3=24 часа выкачивал первый насос остаток воды

24+4=за 28 часов была выкачана вся вода из котлована

Answer 2

Problem Analysis

We are given two pumps, one of which can pump all the water out of a pit in 36 hours, while the other pump is twice as fast. After working together and pumping out 1/3 of the water, the second pump breaks down, and the remaining water is pumped out by the first pump alone. We need to determine how long it took to pump out all the water from the pit.

Solution

Let's assume that the total amount of water in the pit is represented by the variable W. Since the first pump can pump out all the water in 36 hours, its pumping rate can be calculated as W/36 per hour. The second pump is twice as fast, so its pumping rate is 2W/36 per hour, which simplifies to W/18 per hour.

When the two pumps work together, their combined pumping rate is the sum of their individual pumping rates. Therefore, the combined pumping rate is (W/36) + (W/18) = (2W + W)/36 = 3W/36 = W/12 per hour.

After working together, the two pumps manage to pump out 1/3 of the water, which is (1/3)W. This means that the time it took to pump out 1/3 of the water is (1/3)W / (W/12) = (1/3) * (12/1) = 4 hours.

After the second pump breaks down, the remaining water is pumped out by the first pump alone. Since the first pump's pumping rate is W/36 per hour, the time it takes to pump out the remaining water is (2/3)W / (W/36) = (2/3) * (36/1) = 24 hours.

Therefore, the total time it took to pump out all the water from the pit is the sum of the time it took to pump out 1/3 of the water and the time it took to pump out the remaining water, which is 4 + 24 = 28 hours.

Answer

It took a total of 28 hours to pump out all the water from the pit.