Question

Через первую трубу бассейн можно наполнить за 10 часов,через вторую за 15 часов.За сколько часов наполнится бассейн при совместной работе

Answer 1

Это легко 10+15=25(ч)

Answer 2

Х - полный объем бассейна
х/10 - производительность 1 трубы за час
х/15 - производительность второй трубы за час
(х / 10 + х/15) = 3х/30 + 2х/30 = 5х/30 = х/6 - производительность обеих труб за 1 час
При совместной работе обе трубы заполнят бассейн за : х / х/6 = 6 часов

Answer 3

Problem Analysis

We are given two pipes, one of which can fill a pool in 10 hours and the other in 15 hours. We need to determine how long it will take to fill the pool when both pipes are working together.

Solution

To solve this problem, we can use the concept of work rates. The work rate of a pipe is defined as the amount of work it can complete in a given unit of time. In this case, the work rate of the first pipe is 1/10 of the pool per hour, and the work rate of the second pipe is 1/15 of the pool per hour.

When both pipes are working together, their work rates are additive. Therefore, the combined work rate of both pipes is (1/10 + 1/15) of the pool per hour.

To find the time it takes to fill the pool when both pipes are working together, we can use the formula:

Time = 1 / Combined Work Rate

Let's calculate the combined work rate and the time it takes to fill the pool.

Calculation

The combined work rate of both pipes is (1/10 + 1/15) of the pool per hour.

Combined Work Rate = 1/10 + 1/15

To add these fractions, we need to find a common denominator, which is 30.

Combined Work Rate = (3/30 + 2/30) = 5/30

Therefore, the combined work rate of both pipes is 5/30 of the pool per hour.

Now, let's calculate the time it takes to fill the pool using the formula:

Time = 1 / Combined Work Rate

Time = 1 / (5/30)

To divide by a fraction, we can multiply by its reciprocal.

Time = 1 * (30/5)

Time = 30/5

Simplifying the fraction, we get:

Time = 6 hours

Therefore, it will take 6 hours to fill the pool when both pipes are working together.

Answer

The pool will be filled in 6 hours when both pipes are working together.