Question

Три насоса разной мощности могут выкачать воду из бассейна за 4 часа.Первый, работая один,за 12 часов,второй за 16 часов.Какую часть выкачает третий насос,работая один,3 часа?

Answer 1

1 - объем бассейна
Исходя из написанного в условии задачи получим:
$\frac{1}{12}$ басс/ч - производительность первого насоса.
$\frac{1}{16}$ басс/ч - производительность второго насоса.
Пусть х басс/ч - производительность третьего насоса.
тогда $4*( \frac{1}{12}+ \frac{1}{16}+x)=1$
$\frac{1}{3}+ \frac{1}{4}+4x=1 \\ 4x=1-\frac{7}{12} \\ 4x=\frac{5}{12} \\ x=\frac{5}{48}$
Производительность третьего насоса $\frac{5}{48}$ басс/ч.
За 3 часа он выкачает $3*\frac{5}{48}=\frac{5}{16}$ бассейна.

Answer 2

Calculating the Pumping Rates

To calculate the portion of water the third pump can pump in 3 hours, we can use the rates at which each pump works.

- The first pump can pump the entire pool in 12 hours. - The second pump can pump the entire pool in 16 hours. - The third pump, working alone, can pump the entire pool in 4 hours.

Calculating the Portion Pumped by the Third Pump

To find out what portion of the pool the third pump can pump in 3 hours, we can use the concept of work rates. The work rate is inversely proportional to the time taken. Therefore, the portion pumped by the third pump in 3 hours can be calculated using the formula:

portion pumped = (time taken by the third pump / time taken by all pumps working together) * (1 / third pump's individual rate)

Substituting the given values: portion pumped = (3 / 4) * (1 / third pump's rate)

Now, we can calculate the portion pumped by the third pump in 3 hours.