Question

Катер прошел 36 км по течению и 8 км против течения, затратив на весь путь 2 часа. Найдите скорость по течению реки, если собственная скорость катера 20 км/ч, а скорость течения не превосходит 5 км/ч.

Answer 1

Ответ:

Примем за Х собственную скорость катера в км/ч, тогда его скорость по течению (х+2) км/ч

Так как катер прошёл по течению 36 км, то затратил времени 36/(х+2) часа

16 км по озеру катер прошёл за 16/х часов

Так как общее время равно 3 часа, то получаем уравнение:

36/(х+2)+16/х=3

36х+16(х+2)=3х(х+2)

36х+16х+32-3х^2-6х=0

-3х^2+46х+32=0

3х^2-46х-32=0

D=2116+12*32=50^2

X1=(46-50)/6=-2/3 не подходит

Х2=(46+50)/6=16 км/ч

Объяснение:

Answer 2

Problem Analysis

We are given that a boat traveled 36 km downstream and 8 km upstream, taking a total of 2 hours for the entire journey. We need to find the speed of the river's current, given that the boat's own speed is 20 km/h and the speed of the current does not exceed 5 km/h.

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 speed downstream is (20 + 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 speed upstream is (20 - x) 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 the equation: 36 = (20 + x) × t1 ----(1)

The time taken to travel upstream is given by the equation: 8 = (20 - x) × t2 ----(2)

We are also given that the total time for the journey is 2 hours: t1 + t2 = 2 ----(3)

We can solve this system of equations to find the value of x.

Solution Steps

1. Rearrange equation (1) to solve for t1: t1 = 36 / (20 + x)

2. Rearrange equation (2) to solve for t2: t2 = 8 / (20 - x)

3. Substitute the values of t1 and t2 into equation (3): 36 / (20 + x) + 8 / (20 - x) = 2

4. Solve the equation for x.

Let's solve the equation to find the value of x.

Calculation

Substituting the values of t1 and t2 into equation (3), we get: 36 / (20 + x) + 8 / (20 - x) = 2

Multiplying through by the least common denominator, we get: 36(20 - x) + 8(20 + x) = 2(20 + x)(20 - x)

Simplifying the equation, we get: 720 - 36x + 160 + 8x = 2(400 - x^2)

Combining like terms, we get: 880 - 28x = 800 - 2x^2

Rearranging the equation, we get: 2x^2 - 28x + 80 = 0

Factoring the quadratic equation, we get: (2x - 4)(x - 20) = 0

Setting each factor equal to zero, we get: 2x - 4 = 0 or x - 20 = 0

Solving for x, we get: x = 2 or x = 20

Since the speed of the current cannot exceed 5 km/h, the valid solution is x = 2 km/h.

Answer

The speed of the river's current is 2 km/h.