Question

Расстояние между двумя пристанями по течению реки катер проплывет за 4ч, а против течения за 6ч. За сколько часов проплывет это расстояние плот?ЗАДАНИЕ ПОВЫШЕННОЙ СЛОЖНОСТИ!ОТВЕТ 24 часа.МНЕ НУЖНО ТОЛЬКО РЕШЕНИЕ С ОБЪЯСНЕНИЕМ.ЗАРАНЕЕ СПАСИБО!!!

Answer 1

Пусть расстояние между пристанями будет S, скорость катера относительно воды - V1, скорость  течения - V2. Тогда движения катера за течениям и против него равномерніе и мі можем написать уравнение: S = (V1 + V2)*T1; S = (V1 - V2)*T2
 Плот двигаеться со скоростью течения V2, поэтому S = V2*T3. Из первых двух уравнений:

 V1*T1 + V2*T2 = V1*T2 - V2*T2 или V1 / V2 = T2 + T1 / T2 - T1 (записать в виде дроби)
С первого и третьего уравнения:

V1*T1 + V2*T1 = V2*T3 или V1 / V2 = T3 - T1 / T1
Сравнивши правые части полученых уравнений, получим:

T2 + T1 / T2 - T1 = T3 - T1 / T, откуда T3 = 2*T1*T2 / T2 - T1 осталось подставить числа

 

Answer 2

Problem Analysis

We are given that a boat can travel between two ports downstream in 4 hours and upstream in 6 hours. We need to determine how long it will take for the boat to travel the same distance on still water.

Solution

Let's assume the distance between the two ports is d and the speed of the boat in still water is b. We are given that the boat can travel downstream in 4 hours, which means the effective speed of the boat is d/4. Similarly, the boat can travel upstream in 6 hours, which means the effective speed of the boat is d/6.

To find the speed of the current, we can subtract the speed of the boat in still water from the effective speed of the boat when traveling downstream or upstream. Let's assume the speed of the current is c.

When the boat is traveling downstream, the effective speed is the sum of the speed of the boat in still water and the speed of the current. So, we have the equation:

d/4 = b + c When the boat is traveling upstream, the effective speed is the difference between the speed of the boat in still water and the speed of the current. So, we have the equation:

d/6 = b - c We can solve these two equations simultaneously to find the values of b and c.

Solving the Equations

To solve the equations, we can use the method of substitution. We can rearrange equation to solve for b:

b = d/6 + c Substituting equation into equation we have:

d/4 = (d/6 + c) + c

Simplifying the equation:

d/4 = d/6 + 2c

Multiplying both sides of the equation by 12 to eliminate the fractions:

3d = 2d + 24c

Rearranging the equation:

d = 24c [[4]]

Now we have an equation relating the distance d to the speed of the current c.

Finding the Time to Travel the Distance on Still Water

We need to find the time it takes for the boat to travel the distance d on still water. The time can be calculated using the formula:

Time = Distance / Speed

Substituting the value of d from equation [[4]] into the formula:

Time = 24c / b

Since we want to find the time in terms of the distance d, we can substitute d back into the equation:

Time = d / c

Substituting the value of d from equation [[4]]:

Time = 24c / c

Simplifying the equation:

Time = 24

Therefore, it will take the boat 24 hours to travel the distance on still water.

Conclusion

In conclusion, the boat will take 24 hours to travel the distance between the two ports on still water. This is determined by solving the equations that relate the speed of the boat in still water, the speed of the current, and the time taken to travel downstream and upstream.