Question

Два насоса, работая одновременно, могут откачать воду из резервуара за 6 ч. Первый насос , работая один может откачать эту воду за 15 ч. За сколько часов сможет откачать воду из резервуара второй насос, если будет работать только он?

Answer 1

Пусть второй насос, работая отдельно, может накачать воду за х ч, тогда
производительность первого насоса 1/15 , а произв второго 1/х, значит за 6 ч каждый из них выполнит 6/15 и 6/х часть работы, поэтому 
6/15 + 6/x = 1
6/x = 1 - 6/15
6/x = 9/15
x = 6 : 9/15
x = 6 * 15/9
x = 10 (x) может накачать второй, работая отдельно

Answer 2

Problem Analysis

We are given that two pumps can drain water from a reservoir in 6 hours when they work together. We are also given that the first pump alone can drain the water from the reservoir in 15 hours. We need to determine how many hours it will take for the second pump to drain the water from the reservoir if it works alone.

Solution

Let's assume that the rate at which the first pump can drain the water from the reservoir is x units per hour, and the rate at which the second pump can drain the water from the reservoir is y units per hour.

According to the problem, when both pumps work together, they can drain the water from the reservoir in 6 hours. This can be expressed as:

1/x + 1/y = 1/6 We are also given that the first pump alone can drain the water from the reservoir in 15 hours. This can be expressed as:

1/x = 1/15 To find the time it will take for the second pump to drain the water from the reservoir alone, we need to solve the system of equations formed by equations and.

Let's solve the system of equations:

1/x + 1/y = 1/6 1/x = 1/15 From equation we can solve for x:

x = 15

Substituting the value of x into equation we can solve for y:

1/15 + 1/y = 1/6

Multiplying both sides of the equation by 90y, we get:

6y + 90 = 15y

Simplifying the equation, we get:

9y = 90

Dividing both sides of the equation by 9, we get:

y = 10

Therefore, the second pump can drain the water from the reservoir alone in 10 hours.

Answer

If the second pump works alone, it will take 10 hours to drain the water from the reservoir.

References

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