Question

Первый кран наполняет бассейн за 24 часа , второй за 48 ,третий за 72 , четвертый за 96 . Если одновременно включить все четыре крана за сколько времени они наполнят бассейн.

Answer 1

Чтобы решать задачи на совместную работу нужно помнить формулу

А=V*t, где А- работа, t- время, V-производительность (или скорость)

теперь по условию Работа= бассейн примем за 1 (один бассейн)

тогда первый кран наполняет его за 24 часа (время), значит его производительность 1/24 части бассейна за 1 час (скорость)

Второй кран имеет скорость 1/48 части бассейна за 1 час

Третий кран имеет скорость 1/72 части бассейна за 1 час

Четвертый кран имеет скорость 1/96 часть за 1 час

Если Все краны работаю одновременно то тогда за 1 час наполняется

1/24+ 1/48+ 1/72+ 1/96 части бассейна (или совместная скорость)

1/24+1/48+1/72+1/96= (12+6+4+3)/288= 25/288 Скорость

Теперь А=V*t значит t=A/V

t= 1/ (25/288)=288/25=11.52 часа

Answer 2

Problem Analysis

We are given four taps that fill a pool in different amounts of time: the first tap fills the pool in 24 hours, the second tap fills it in 48 hours, the third tap fills it in 72 hours, and the fourth tap fills it in 96 hours. We need to determine how long it will take to fill the pool if all four taps are turned on simultaneously.

Solution

To solve this problem, we need to find the combined rate at which the four taps fill the pool. We can calculate this by finding the sum of the rates of each tap.

Let's denote the rate at which the first tap fills the pool as r1, the rate of the second tap as r2, the rate of the third tap as r3, and the rate of the fourth tap as r4.

The rate at which each tap fills the pool can be calculated by taking the reciprocal of the time it takes for each tap to fill the pool. For example, the rate of the first tap (r1) is 1/24, the rate of the second tap (r2) is 1/48, the rate of the third tap (r3) is 1/72, and the rate of the fourth tap (r4) is 1/96.

To find the combined rate, we sum up the rates of all four taps:

Combined rate = r1 + r2 + r3 + r4

Finally, we can calculate the time it takes to fill the pool by taking the reciprocal of the combined rate:

Time to fill the pool = 1 / (r1 + r2 + r3 + r4)

Let's calculate the time it takes to fill the pool:

r1 = 1/24

r2 = 1/48

r3 = 1/72

r4 = 1/96

Combined rate = r1 + r2 + r3 + r4

Time to fill the pool = 1 / (r1 + r2 + r3 + r4)

Calculation

r1 = 1/24 = 0.0417

r2 = 1/48 = 0.0208

r3 = 1/72 = 0.0139

r4 = 1/96 = 0.0104

Combined rate = 0.0417 + 0.0208 + 0.0139 + 0.0104 = 0.0868

Time to fill the pool = 1 / 0.0868 = 11.51 hours

Therefore, if all four taps are turned on simultaneously, it will take approximately 11.51 hours to fill the pool.

Answer

If all four taps are turned on simultaneously, they will fill the pool in approximately 11.51 hours.