Question

Один кран наполняет бассейн на 3 ч быстрее другого, 2 крана работая вместе наполняют бассейн за 2ч . За сколько часов может наполнить бассейн каждый кран.

Answer 1

Ответ:

За 5 часов можно наполнить бассейн

Answer 2

Ответ:

за 6минут можно наполнить весь басейн

Answer 3

Problem Analysis

We are given that one faucet fills a pool 3 hours faster than another faucet, and when both faucets are used together, they can fill the pool in 2 hours. We need to determine how long it would take each faucet to fill the pool individually.

Solution

Let's assume that the slower faucet takes x hours to fill the pool. According to the given information, the faster faucet takes x - 3 hours to fill the pool.

When both faucets are used together, they can fill the pool in 2 hours. This means that in 1 hour, they can fill 1/2 of the pool.

To find the individual rates of each faucet, we can set up the following equation:

1/x + 1/(x - 3) = 1/2

We can solve this equation to find the value of x, which represents the time taken by the slower faucet to fill the pool.

Calculation

To solve the equation 1/x + 1/(x - 3) = 1/2, we can use algebraic manipulation.

Multiplying both sides of the equation by 2x(x - 3) to eliminate the denominators, we get:

2(x - 3) + 2x = x(x - 3)

Simplifying the equation:

2x - 6 + 2x = x^2 - 3x

Combining like terms:

4x - 6 = x^2 - 3x

Rearranging the equation:

x^2 - 7x + 6 = 0

Factoring the quadratic equation:

(x - 6)(x - 1) = 0

Setting each factor equal to zero:

x - 6 = 0 or x - 1 = 0

Solving for x:

x = 6 or x = 1

Since the slower faucet cannot fill the pool in 1 hour (as the faster faucet takes x - 3 hours), we can conclude that the slower faucet takes 6 hours to fill the pool.

Therefore, the faster faucet takes 6 - 3 = 3 hours to fill the pool.

Answer

The slower faucet takes 6 hours to fill the pool, while the faster faucet takes 3 hours to fill the pool.