Question

Из горячего крана ванна заполняется за 23 мин, из холодного - за 17 мин. Сначала был открыт горячий кран. Через сколько минут надо открыть холодный кран, чтобы к моменту наполнения ванны горячей воды налилось в 1,5 раза больше, чем холодной?

Answer 1

1/23 скорость наплнения горячей водой

1/17 скорость наполнения холодной водой

х мин наливалась горячая
у мин наливалась холодная

составим систему уравнений

$\left \{ {{\frac{x}{23}+\frac{y}{17}=1} \atop {\frac{x}{23}=\frac{1,5y}{17}}} \right.$

$\left \{ {{\frac{x}{23}}=1- \frac{y}{17 } \atop {\frac{x}{23}=\frac{1,5y}{17}}} \right.$


1,5у/17=1-у/17
1,5у/17=(17-у)/17
1,5у=17-у
2,5у=17
у=17/2,5=6,8 мин холодная

х/23=1-6,8/17
х/23=0,6
х=0,6*23=13,8

13,8-6,8=7 мин

Ответ через 7 мин нужно открыть холодную воду 

 

Answer 2

Problem Analysis

We are given that a bathtub fills up from the hot faucet in 23 minutes and from the cold faucet in 17 minutes. The hot faucet was opened first, and we need to determine how many minutes we should open the cold faucet so that by the time the bathtub is filled with hot water, there will be 1.5 times more hot water than cold water.

Solution

To solve this problem, we can set up an equation based on the rates at which the hot and cold faucets fill the bathtub. Let's assume that the rate at which the hot faucet fills the bathtub is H (in units of bathtub volume per minute) and the rate at which the cold faucet fills the bathtub is C (in units of bathtub volume per minute).

We are given that the hot faucet fills the bathtub in 23 minutes, so we can write the equation: H * 23 = 1 (equation 1)

Similarly, we are given that the cold faucet fills the bathtub in 17 minutes, so we can write the equation: C * 17 = 1 (equation 2)

We need to find the number of minutes it takes for the cold faucet to fill 1.5 times more water than the hot faucet. Let's assume this time is T (in minutes). At time T, the amount of water filled by the hot faucet is H * T, and the amount of water filled by the cold faucet is C * T.

According to the problem, we want the amount of hot water to be 1.5 times more than the amount of cold water, so we can write the equation: H * T = 1.5 * (C * T) (equation 3)

To solve for T, we can substitute equations 1 and 2 into equation 3 and solve for T.

Calculation

Let's solve the equations to find the value of T.

From equation 1, we have: H = 1/23

From equation 2, we have: C = 1/17

Substituting these values into equation 3, we get: (1/23) * T = 1.5 * (1/17) * T

Simplifying the equation, we have: 1/23 = 1.5/17

Cross-multiplying, we get: 17 = 1.5 * 23

Dividing both sides by 1.5, we get: T = 17 * 23 / 1.5

Evaluating the expression, we find: T ≈ 261.33

Therefore, we need to open the cold faucet for approximately 261.33 minutes in order to have 1.5 times more hot water than cold water in the bathtub by the time it is filled with hot water.

Answer

To have 1.5 times more hot water than cold water in the bathtub by the time it is filled with hot water, you should open the cold faucet for approximately 261.33 minutes.

Note: The calculated value is an approximation and may vary slightly depending on the specific rates at which the faucets fill the bathtub.