Question

Для наполнения бассейна открыли 3 крана. 1 кран за 12 ч, 2 кран за 8 ч, 3 кран за 15 ч. За какое время заполняет бассейн все 3 крана? ​

Answer 1

Ответ:

х - Объем бассейна

х/12 - часовая производительность первого крана

х/8 - часовая производительность второго крана

х/15 - часовая производительность третьего крана

х /12 + х /8 + х /15 = 10х/120 +15х/120 + 8х/120 = 33х/120 = 11х/40 - часовая производительность всех трех кранов . Значит они за 1 час заполнят бассейн на 11/40 часть от объема

Пошаговое объяснение:

Answer 2

To find out how much time it takes to fill the pool when all three faucets are open, we need to calculate the combined rate of water flow from all three faucets.

Let's denote:

• The rate of the first faucet (1 кран) as R1 (in pool volume per hour).
• The rate of the second faucet (2 кран) as R2 (in pool volume per hour).
• The rate of the third faucet (3 кран) as R3 (in pool volume per hour).

We are given the following information:

1. The first faucet fills the pool in 12 hours: R1 = 1 pool volume / 12 hours = 1/12 pool volume per hour.

2. The second faucet fills the pool in 8 hours: R2 = 1 pool volume / 8 hours = 1/8 pool volume per hour.

3. The third faucet fills the pool in 15 hours: R3 = 1 pool volume / 15 hours = 1/15 pool volume per hour.

Now, to find the combined rate of all three faucets (R_total), we add up their individual rates:

R_total = R1 + R2 + R3 R_total = 1/12 + 1/8 + 1/15

To add these fractions, we need to find a common denominator, which is 120:

R_total = (10/120) + (15/120) + (8/120) R_total = 33/120

Now we can simplify the fraction:

R_total = 11/40 pool volume per hour

Now that we know the combined rate of all three faucets, we can find the time it takes to fill the pool (T_total) using the formula:

T_total = Total pool volume / R_total

Since we want to fill one pool volume, the total pool volume is 1:

T_total = 1 / (11/40) T_total = 40/11

So, the time it takes to fill the pool when all three faucets are open is approximately 3.64 hours, which is approximately 3 hours and 39 minutes.