Question

Катер проплыл 7 км по течению реки и 24 км против течения той же реки за 1 час 15 минут.Найдите скорость течения реки если собственная скорость катера 26 км/ч.

Answer 1

пусть скорость течения х км/ч, тогда скорость по течению 26+х, против течения 26-х.

Время по течению 7/(26+x),  против течения  24/(26-x). Уравнение

7/(26+x) +24/(26-х) = 5/4,   после упрощения:   5x^2 + 68x - 156 = 0

x=-15,6 не подходит по смыслу задачи;   x=2, т.е. скорость течения реки 2 км/ч

Answer 2

Problem Analysis

We are given the following information: - The boat traveled 7 km downstream (with the current) in a certain amount of time. - The boat traveled 24 km upstream (against the current) in the same amount of time. - The boat's own speed is 26 km/h.

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 boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's effective speed downstream is (26 + x) km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's effective speed upstream is (26 - x) km/h.

We are given that the boat traveled 7 km downstream and 24 km upstream in a total time of 1 hour and 15 minutes, which is equivalent to 1.25 hours.

Using the formula distance = speed × time, we can set up the following equations:

Equation 1: 7 = (26 + x) × 1.25 (for the downstream journey) Equation 2: 24 = (26 - x) × 1.25 (for the upstream journey)

Let's solve these equations to find the value of x.

Calculation

Solving Equation 1: 7 = (26 + x) × 1.25 Dividing both sides by 1.25: 5.6 = 26 + x Subtracting 26 from both sides: x = 5.6 - 26 x = -20.4

Solving Equation 2: 24 = (26 - x) × 1.25 Dividing both sides by 1.25: 19.2 = 26 - x Subtracting 26 from both sides: -6.8 = -x Multiplying both sides by -1: 6.8 = x

Answer

The speed of the river's current is 6.8 km/h.

Verification

Let's verify our answer by substituting the value of x into the original equations:

Equation 1: 7 = (26 + 6.8) × 1.25 7 = 32.8 × 1.25 7 = 41

Equation 2: 24 = (26 - 6.8) × 1.25 24 = 19.2 × 1.25 24 = 24

Both equations are true, which confirms that our answer is correct.