Question

В резервуар проведены две трубы. Через первую вода втекает со скоростью 40 куб.дм. в минуту, а через вторую вытекает 900 куб.дм. в час. Если открыть обе трубы одновременно, то пустой резервуар наполнится через 6 ч. Найти вместимость резервуара.

Answer 1

Problem Analysis

We are given a situation where there are two pipes connected to a reservoir. Water flows into the reservoir through the first pipe at a rate of 40 cubic decimeters per minute, and water flows out of the reservoir through the second pipe at a rate of 900 cubic decimeters per hour. If both pipes are opened simultaneously, the empty reservoir will be filled in 6 hours. We need to find the capacity of the reservoir.

Solution

Let's assume the capacity of the reservoir is C cubic decimeters.

The rate at which water flows into the reservoir through the first pipe is 40 cubic decimeters per minute. Therefore, the rate of inflow can be expressed as 40/60 cubic decimeters per second.

The rate at which water flows out of the reservoir through the second pipe is 900 cubic decimeters per hour. Therefore, the rate of outflow can be expressed as 900/3600 cubic decimeters per second.

When both pipes are opened simultaneously, the net rate of inflow into the reservoir is the difference between the rate of inflow and the rate of outflow. This can be expressed as:

(40/60) - (900/3600) cubic decimeters per second.

We are given that the empty reservoir will be filled in 6 hours. Therefore, the time taken to fill the reservoir is 6 hours, which is equal to 6 x 3600 seconds.

Using the formula rate x time = volume, we can set up the equation:

(40/60 - 900/3600) x (6 x 3600) = C

Simplifying the equation:

(2/3 - 1/4) x 21600 = C

C = (8/12 - 3/12) x 21600

C = (5/12) x 21600

C = 9000 cubic decimeters

Therefore, the capacity of the reservoir is 9000 cubic decimeters.

Answer

The capacity of the reservoir is 9000 cubic decimeters.