Question

Расстояние между двумя пристанями по реке равно 24 км. Моторная лодка прошла от одной пристани до другой, сдалала стоянку на 1 ч 40 мин и вернулась обратно. Все путешествие заняло 6 2/3 ч. Найдите скорость течения реки, ксли известно, что скорость моторной лодки в стоячей воде равна 10 км

Answer 1

Решение Вашей задачи во вложении

 

Answer 2

как то так)это 22 задание ведь?

Answer 3

Problem Analysis

We are given that the distance between two piers on a river is 24 km. A motorboat traveled from one pier to the other, made a stop for 1 hour and 40 minutes, and then returned back. The total duration of the trip was 6 and 2/3 hours. We need to find the speed of the river current, given that the speed of the motorboat in still water is 10 km/h.

Solution

Let's assume the speed of the river current is v km/h.

When the motorboat is traveling downstream (from the first pier to the second), it benefits from the speed of the river current. Therefore, the effective speed of the motorboat is the sum of its speed in still water and the speed of the river current.

When the motorboat is traveling upstream (from the second pier back to the first), it opposes the speed of the river current. Therefore, the effective speed of the motorboat is the difference between its speed in still water and the speed of the river current.

We can use the formula: distance = speed × time to calculate the time taken for each leg of the journey.

Let's calculate the time taken for the downstream journey first. The distance traveled downstream is 24 km, and the effective speed of the motorboat is the sum of its speed in still water (10 km/h) and the speed of the river current (v km/h). Therefore, the time taken for the downstream journey is:

time_downstream = distance / (10 + v)

Next, let's calculate the time taken for the upstream journey. The distance traveled upstream is also 24 km, but the effective speed of the motorboat is the difference between its speed in still water (10 km/h) and the speed of the river current (v km/h). Therefore, the time taken for the upstream journey is:

time_upstream = distance / (10 - v)

The total duration of the trip is given as 6 and 2/3 hours. We can convert this to an improper fraction: 6 and 2/3 = (6 × 3 + 2) / 3 = 20/3 hours. Therefore, the total time taken for the trip is:

total_time = time_downstream + 1 hour and 40 minutes + time_upstream

We can convert 1 hour and 40 minutes to hours by dividing it by 60: 1 hour and 40 minutes = (1 + 40/60) hours = 1.67 hours.

Now, we can substitute the values into the equation and solve for v:

20/3 = distance / (10 + v) + 1.67 + distance / (10 - v)

Simplifying the equation, we get:

20/3 = 24 / (10 + v) + 1.67 + 24 / (10 - v)

To solve this equation, we can multiply both sides by (10 + v)(10 - v) to eliminate the denominators:

20/3 * (10 + v)(10 - v) = 24 * (10 - v) + 1.67 * (10 + v) + 24 * (10 + v)

Simplifying further, we get:

20/3 * (100 - v^2) = 24 * (10 - v) + 1.67 * (10 + v) + 24 * (10 + v)

Expanding and rearranging the equation, we get:

2000/3 - 20/3 * v^2 = 240 - 24v + 16.7 + 1.67v + 240 + 24v

Combining like terms, we get:

2000/3 - 20/3 * v^2 = 480 + 1.67v + 240

Simplifying further, we get:

2000/3 - 20/3 * v^2 = 720 + 1.67v

Multiplying both sides by 3 to eliminate the fractions, we get:

2000 - 20v^2 = 2160 + 5v

Rearranging the equation, we get:

20v^2 + 5v - 160 = 0

Now, we can solve this quadratic equation for v using the quadratic formula:

v = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c into the formula, we get:

v = (-5 ± √(5^2 - 4 * 20 * -160)) / (2 * 20)

Simplifying further, we get:

v = (-5 ± √(25 + 12800)) / 40

v = (-5 ± √12825) / 40

Taking the positive root, we get:

v = (-5 + √12825) / 40

Calculating the value, we get:

v ≈ 3.75 km/h

Therefore, the speed of the river current is approximately 3.75 km/h.

Answer

The speed of the river current is approximately 3.75 km/h.