Question

От двух пристаней, расстояние между которыми равно 82 км, навстречу друг другу движутся по реке две моторные лодки. Лодка, идущая по течению, собственная скорость которой равна 20 км/ч, до встречи шла 2 ч, другая лодка, собственная скорость которой равна 15 км/ч, до встречи шла 3 ч. Найдите скорость течения реки.

Answer 1

Ответ:

3 км/ч.

Пошаговое объяснение:

Пусть х км/ч - скорость течения реки; х >0;

Тогда:

2(20+х) км - проплыла первая лодка;

3(15-х) км - проплыла вторая лодка.

Зная,что всего обе лодки проплыли 82 км, состасим и решим уравнение.

2(20+х)+3(15-х)=82;

40+2х+45-3х=82;

2х-3х=82-40-45;

-х=-3;

х=3;

3>0 - верно;

3 км/ч - скорость течения.

Answer 2

Problem Analysis

We are given two motorboats moving towards each other on a river. The distance between the two piers is 82 km. One boat is moving downstream with a speed of 20 km/h and took 2 hours to meet the other boat. The second boat is moving upstream with a speed of 15 km/h and took 3 hours to meet the first boat. We need to find the speed of the river's current.

Solution

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

When the first boat is moving downstream, its effective speed is the sum of its own speed and the speed of the river's current. So, the effective speed of the first boat is (20 + x) km/h.

Similarly, when the second boat is moving upstream, its effective speed is the difference between its own speed and the speed of the river's current. So, the effective speed of the second boat is (15 - x) km/h.

We can use the formula: distance = speed × time to find the distance traveled by each boat.

For the first boat: - Distance traveled = (20 + x) km/h × 2 h

For the second boat: - Distance traveled = (15 - x) km/h × 3 h

Since the two boats meet each other, the sum of their distances traveled should be equal to the total distance between the piers, which is 82 km.

Therefore, we can set up the following equation: (20 + x) × 2 + (15 - x) × 3 = 82

Now, let's solve this equation to find the value of x.

Calculation

Expanding the equation: 40 + 2x + 45 - 3x = 82

Combining like terms: 85 - x = 82

Simplifying: -x = -3

Dividing both sides by -1: x = 3

Answer

The speed of the river's current is 3 km/h.

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