Question

Через2 крана бак наполнился за 15мин. Еслибы бы открыт только 1 кран то бы бак наполнился за 24 мин. За сколько мир наполнился бы бак через 1-2кран

Answer 1

Problem Analysis

We are given that a tank can be filled by two taps in 15 minutes and by one tap in 24 minutes. We need to determine how long it would take to fill the tank if both taps are open.

Solution

Let's assume that the rate at which the first tap fills the tank is x liters per minute, and the rate at which the second tap fills the tank is y liters per minute.

According to the given information, the tank can be filled by both taps in 15 minutes. This means that in 1 minute, the combined rate of both taps is equal to 1/15 of the tank's capacity.

Similarly, when only one tap is open, the tank can be filled in 24 minutes. This means that in 1 minute, the rate of that tap is equal to 1/24 of the tank's capacity.

Let's set up the equations based on the above information:

Equation 1: x + y = 1/15 (combined rate of both taps) Equation 2: x = 1/24 (rate of one tap)

To solve these equations, we can substitute the value of x from Equation 2 into Equation 1:

1/24 + y = 1/15

Now, we can solve this equation to find the value of y.

Calculation

Let's solve the equation:

1/24 + y = 1/15

To add the fractions, we need to find a common denominator. The least common multiple of 24 and 15 is 120.

Multiplying both sides of the equation by 120, we get:

5 + 120y = 8

Subtracting 5 from both sides, we have:

120y = 3

Dividing both sides by 120, we find:

y = 3/120 = 1/40

Now, we know the value of y. Let's substitute it back into Equation 2 to find the value of x:

x = 1/24

Therefore, the value of x is 1/24.

Conclusion

We have found that the rate at which the first tap fills the tank is 1/24 liters per minute, and the rate at which the second tap fills the tank is 1/40 liters per minute.

To find the time it would take to fill the tank when both taps are open, we can add the rates of both taps:

1/24 + 1/40 = 5/120 + 3/120 = 8/120 = 1/15

Therefore, the tank would be filled in 15 minutes when both taps are open.

Please let me know if anything is unclear or if you need further assistance!