Question

Расстояние между двумя пристанями на реке равно 21 км. Моторная лодка отправилась от одной пристани до другой и через 4 часа вернулась назад, затратив на стоянку 24 мин. Найдите скорость моторной лодки, если скорость течения реки равна 2 км/ч.

Answer 1

S=21км
составляем мат.модель задачи
21/(x+2)+21/(x-2)+2/5=4
откуда х=12км/ч - скорость моторной лодки

Answer 2

Problem Analysis

We are given that the distance between two piers on a river is 21 km. A motorboat travels from one pier to the other and returns back after 4 hours, including a 24-minute stop. We need to find the speed of the motorboat, given that the river's current speed is 2 km/h.

Solution

To find the speed of the motorboat, we can use the formula:

Speed = Distance / Time

Let's calculate the time taken by the motorboat to travel from one pier to the other and back, excluding the time spent on the stop.

The time taken to travel from one pier to the other is given by:

Time = Distance / (Speed of the motorboat + Speed of the river's current)

The time taken to return back from the second pier to the first pier is given by:

Time = Distance / (Speed of the motorboat - Speed of the river's current)

Since the total time taken is 4 hours, we can write the equation:

Time + Time + Stop Time = 4 hours

Substituting the values, we get:

(Distance / (Speed of the motorboat + Speed of the river's current)) + (Distance / (Speed of the motorboat - Speed of the river's current)) + Stop Time = 4 hours

Simplifying the equation, we get:

2 * Distance / (Speed of the motorboat + Speed of the river's current) + Stop Time = 4 hours

Now, we can substitute the given values:

2 * 21 km / (Speed of the motorboat + 2 km/h) + 24 minutes = 4 hours

Converting the stop time to hours:

2 * 21 km / (Speed of the motorboat + 2 km/h) + 24/60 hours = 4 hours

Simplifying further:

2 * 21 km / (Speed of the motorboat + 2 km/h) + 0.4 hours = 4 hours

Now, we can solve this equation to find the speed of the motorboat.

Let's calculate the speed of the motorboat using the given equation.

Calculation

Substituting the values into the equation:

2 * 21 km / (Speed of the motorboat + 2 km/h) + 0.4 hours = 4 hours

Simplifying the equation:

42 km / (Speed of the motorboat + 2 km/h) + 0.4 hours = 4 hours

Multiplying both sides by (Speed of the motorboat + 2 km/h):

42 km + 0.8 km = 4 hours * (Speed of the motorboat + 2 km/h)

Simplifying further:

42.8 km = 4 hours * (Speed of the motorboat + 2 km/h)

Dividing both sides by 4 hours:

42.8 km / 4 hours = Speed of the motorboat + 2 km/h

Simplifying further:

10.7 km/h = Speed of the motorboat + 2 km/h

Subtracting 2 km/h from both sides:

10.7 km/h - 2 km/h = Speed of the motorboat

Calculating the speed of the motorboat:

Speed of the motorboat = 8.7 km/h

Therefore, the speed of the motorboat is 8.7 km/h.

Answer

The speed of the motorboat is 8.7 km/h.