Question

Два насоса заполняют одинаковые бассейны, по 80 тонн каждый. Второй насос начал работать на 1 час позднее и качал на 4 тонны в час больше первого. Сколько тонн в час качает первый насос, если они закончили работу одновременно?

Answer 1

Х-качает 1 в час,х+4--качает 2 в час
80/х-80/(х+4)=1
80(х+4-х)=х(х+4)
х²+4х-320=0
х1+х2=-4 и х1*х2=-320
х1=-20-не удов усл
х2=16-качает 1 в час

Answer 2

Скорость первого х,второго х+4, время первого 80/х, второго 80/х+4. первый работал на час дольше, следовательно 80/х-1=80/х+4.
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Answer 3

Problem Analysis

We have two pumps that are filling identical pools, each with a capacity of 80 tons. The second pump starts operating 1 hour later than the first pump and pumps 4 tons more per hour than the first pump. We need to determine the pumping rate of the first pump so that both pumps finish filling their respective pools at the same time.

Solution

Let's assume the pumping rate of the first pump is x tons per hour. Since the second pump pumps 4 tons more per hour than the first pump, the pumping rate of the second pump would be (x + 4) tons per hour.

We know that both pumps fill identical pools with a capacity of 80 tons. The time taken to fill a pool can be calculated by dividing the pool capacity by the pumping rate. Therefore, the time taken by the first pump to fill the pool is 80 / x hours, and the time taken by the second pump is 80 / (x + 4) hours.

Since the second pump starts operating 1 hour later than the first pump, the total time taken by both pumps to fill their respective pools should be the same. Therefore, we can set up the following equation:

80 / x = 80 / (x + 4 - 1)

Simplifying the equation:

80 / x = 80 / (x + 3)

To solve this equation, we can cross-multiply:

80(x + 3) = 80x

Expanding and simplifying:

80x + 240 = 80x

We can see that the variable 'x' cancels out, leaving us with a constant equation:

240 = 0

Since the equation is not true, it means there is no value of 'x' that satisfies the equation. This implies that there is no solution to the problem as stated.

Therefore, it is not possible for both pumps to finish filling their respective pools at the same time, given the conditions provided.

Conclusion

Based on the given information, it is not possible for both pumps to finish filling their respective pools at the same time. The problem statement seems to have a contradiction or an error in the provided information.