Question

5. Решить задачу: Катер прошел по течению реки 8 км, а против течения 3 км, затратив на весь путь 45 минут. Найдите собственную скорость катера, если скорость течения реки равна 2 км/ч.​

Answer 1

Собственная скорость катера 14 км/ч
пусть собственная скорость катера х
8/(x+2)+3/(x-2)=3/4
(8x-16+3x+6)*4=3x^2-12
(11x-10)*4=3x^2-12
44x-40=3x^2-12
3x^2-44x+28=0
x=(22+-20)/3
x>2 x=14

Answer 2

Problem Analysis

We are given that a boat traveled 8 km downstream and 3 km upstream in a total of 45 minutes. The speed of the river current is given as 2 km/h. We need to find the speed of the boat.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. So, the effective speed downstream is (v + 2) km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. So, the effective speed upstream is (v - 2) km/h.

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

The time taken to travel downstream is given by: 8 = (v + 2) × (45/60)

The time taken to travel upstream is given by: 3 = (v - 2) × (45/60)

Simplifying these equations, we get: 8 = (v + 2) × (3/4) 3 = (v - 2) × (3/4) We can solve these two equations to find the value of v.

Calculation

Let's solve the equations and to find the value of v.

From equation 8 = (v + 2) × (3/4)

Multiplying both sides by 4/3: 32/3 = v + 2

Subtracting 2 from both sides: v = 32/3 - 2 = 32/3 - 6/3 = 26/3

So, the speed of the boat in still water is 26/3 km/h.

Answer

The speed of the boat in still water is 26/3 km/h.

Note: The solution provided above is based on the given information and the assumption that the boat's speed remains constant throughout the journey.