Question

Будь ласка решите даю 50 балів через 1 кран басейн наповнюється за 18 хв а через другий за 30 хв 1) чи наповниться під час одночасної роботи обох кранів за 2 хв більше ніж 1/5 басейну? 2) яка частина басейну буде не заповнена водою через 2 хв одночасної роботи обох кранів?

Answer 1

Ответ:

Пошаговое объяснение:

1: 18 =  1/18 частина басейну яка заповнюється за 1 хв через один кран

1 : 30 = 1/30 частина басейну , яка заповнюється за 1 хв. через другий кран  

1/18 + 1/30  = 5/90 + 3/90= 8/90 = 4/45 - частина басейну яка заповниться за одну хвилину, якщо вони працюють  разом

4/45 + 4/45=  9/45 = 1/5   частина басейну, яка заповниться за 2 хв., якщо вони працюють  разом

1)За 2 хв. заповниться не більше 1/5 басейну, а рівно 1/5 басейну

2) 1 - 1/5= 1/5 частина басейну яка не заповнена водою через 2 хв одночасної роботи обох кранів

Answer 2

Calculation of Water Filling Time

To answer the given questions, let's calculate the water filling time for each faucet individually and then determine if the pool will be filled more than 1/5 in 2 minutes.

Given information: - Faucet 1 fills the pool in 18 minutes. - Faucet 2 fills the pool in 30 minutes.

To find the rate at which each faucet fills the pool, we can calculate the inverse of the time taken by each faucet to fill the pool.

The rate at which Faucet 1 fills the pool = 1 pool / 18 minutes = 1/18 pool per minute. The rate at which Faucet 2 fills the pool = 1 pool / 30 minutes = 1/30 pool per minute.

Question 1: Will the pool be filled more than 1/5 in 2 minutes?

To determine if the pool will be filled more than 1/5 in 2 minutes, we need to calculate the combined rate at which both faucets fill the pool.

The combined rate at which both faucets fill the pool = Rate of Faucet 1 + Rate of Faucet 2 = 1/18 + 1/30 = 13/270 pool per minute.

Now, let's calculate the amount of water filled in 2 minutes by both faucets combined:

Amount of water filled in 2 minutes = Combined rate * Time = (13/270) * 2 = 26/270 pool.

To check if this amount is more than 1/5 of the pool, we can compare it to 1/5:

(26/270) > (1/5)

Simplifying the comparison:

26 * 5 > 270

130 > 270

Since 130 is not greater than 270, the pool will not be filled more than 1/5 in 2 minutes when both faucets are working simultaneously.

Question 2: What fraction of the pool will be unfilled after 2 minutes of simultaneous operation of both faucets?

To find the fraction of the pool that will be unfilled after 2 minutes of simultaneous operation of both faucets, we need to subtract the amount of water filled in 2 minutes from the total capacity of the pool.

The total capacity of the pool is not given in the question, so we cannot determine the exact fraction of the pool that will be unfilled. However, we can calculate the fraction based on the given information.

Amount of water filled in 2 minutes = 26/270 pool (calculated in the previous question).

To find the fraction of the pool that will be unfilled, we subtract the amount of water filled from 1 (since 1 represents the full pool):

Fraction of the pool unfilled = 1 - (26/270) = (270/270) - (26/270) = 244/270.

Therefore, after 2 minutes of simultaneous operation of both faucets, approximately 244/270 or 0.9037 (rounded to four decimal places) fraction of the pool will be unfilled.

Please note that the exact fraction of the pool that will be unfilled depends on the total capacity of the pool, which is not provided in the question.