Question

Моторная лодка прошла 39 км по течению и 28 км против течения реки за тоже время,за которое она могла пройти в озере 70 км.Найдите скорость лодки стоячей в воде,если скорость течения реки равна 3 км/ч

Answer 1

Пусть х км/ч - скорость лодки в стоящей воде, тогда скорость против течения равна (х-3) км/ч, а скорость по течению - (x+3) км/ч. Время, затраченное лодкой против течения равно $\dfrac{28}{x-3}$ ч, а по течению $\dfrac{39}{x+3}$ ч. Лодка прошла бы 70 км за $\dfrac{70}{x}$ ч.

Составим уравнение

$\displaystyle \frac{39}{x+3} + \frac{28}{x-3}= \frac{70}{x}$
Умножим обе части уравнения на x(x-3)(x+3) и при этом $x_1\ne 0;~~ x_2\ne 3;~~~ x_3\ne -3$, получаем:
$39x(x-3)+28x(x+3)=70(x-3)(x+3)\\ 39x^2-117x+28x^2+84x=70x^2-630\\ 3x^2+33x-630=0~~~|:3\\ x^2+11x-210=0$
По теореме Виета, получаем корни
$x_1=-21$ - не удовлетворяет условию
$x_2=10$ км/ч - скорость лодки в стоячей воде.

ОТВЕТ: 10 км/ч.

Answer 2

Problem Analysis

We are given the following information: - The motorboat traveled 39 km downstream (with the current) and 28 km upstream (against the current) in the same amount of time. - The boat could travel 70 km in still water (in a lake) in the same amount of time. - The speed of the river current is 3 km/h.

We need to find the speed of the boat in still water.

Solution

Let's assume the speed of the boat in still water is x km/h.

When the boat is traveling downstream (with the current), its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed downstream is (x + 3) km/h.

When the boat is traveling upstream (against the current), its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed upstream is (x - 3) km/h.

We are given that the boat traveled 39 km downstream and 28 km upstream in the same amount of time. We can use the formula time = distance / speed to write the following equation:

39 / (x + 3) = 28 / (x - 3)

To solve this equation, we can cross-multiply and simplify:

39(x - 3) = 28(x + 3)

Simplifying further:

39x - 117 = 28x + 84

39x - 28x = 84 + 117

11x = 201

x = 201 / 11

x ≈ 18.27

Therefore, the speed of the boat in still water is approximately 18.27 km/h.

Answer

The speed of the boat in still water is approximately 18.27 km/h.