Question

Как найти время прохождения пути в стоячей воде, если известно время прохождения по течению (8ч) и против течения (12ч)? Расстояние и скорость одинаковые

Answer 1

1-расстояние
1/8-скорость по течению
1/12-скорость против течения
х-скорость течения
1/8-х=1/12+х
2х=1/8-1/12
2х=3/24-2/24
2х=1/24
х=1/24:2
х=1/24*1/2
х=1/48
1/12+1/48=4/48+1/48=5/48-собственная скорость
1:5/48=1*48/5=48/5=9,6часа
9,6ч=9ч 36мин

Answer 2

Calculating Time of Travel in Still Water

To find the time of travel in still water, given the time of travel with the current and against the current, we can use the concept of relative velocity.

Let's assume the distance traveled is d and the speed of the boat in still water is v.

When traveling with the current, the effective speed of the boat is the sum of the speed of the boat in still water and the speed of the current. Therefore, the time taken to travel the distance d with the current is given by:

Time with current = d / (v + c)

Where c is the speed of the current.

Similarly, when traveling against the current, the effective speed of the boat is the difference between the speed of the boat in still water and the speed of the current. Therefore, the time taken to travel the distance d against the current is given by:

Time against current = d / (v - c)

Given that the time taken to travel with the current is 8 hours and the time taken to travel against the current is 12 hours, we can set up the following equations:

8 = d / (v + c)

12 = d / (v - c)

To solve these equations, we need to eliminate the distance d. We can do this by multiplying the two equations together:

(8 * 12) = (d / (v + c)) * (d / (v - c))

Simplifying this equation gives us:

96 = (d^2) / (v^2 - c^2)

Now, since the distance d and the speed of the boat in still water v are the same for both cases, we can cancel them out:

96 = 1 / (1 - (c^2 / v^2))

Simplifying further:

96 - 96(c^2 / v^2) = 1

96(c^2 / v^2) = 95

Finally, we can solve for the ratio of the speed of the current to the speed of the boat in still water:

(c^2 / v^2) = 95 / 96

Taking the square root of both sides:

c / v = sqrt(95 / 96)

Now, we can substitute this value back into one of the original equations to find the value of v or c. However, since the question states that the distance and speed are the same, we can assume that the speed of the boat in still water is equal to the speed of the current:

v = c

Therefore, the speed of the boat in still water is equal to the speed of the current, and we can calculate the value using the square root of 95/96.

v = c = sqrt(95 / 96)

Please note that the actual numerical value of the speed of the boat in still water and the current cannot be determined without additional information.