Question

Катер прошел 18км по течению речки,а потом 20км против течения, потратив на весь путь 2 часа. Найдите скорость течения, если собственная скорость катера равна 20км в час.

Answer 1

T1=18/(20+x)- время по течению.
t2=20/(20-x)- время против течения.
t1+t2=2
18/(20+x)+20/(20-x)=2
18(20-x)+20(20+x)=2(20^2-x^2
360-18х+400+20х=800-2х^2
2х^2+2х-40=0. разделим все на 2.
х^2+х-20=0
х1=-5. х2=4
ответ: 4 км/ч скорость реки.

Answer 2

Problem Analysis

We are given that a boat traveled 18 km downstream and then 20 km upstream, taking a total of 2 hours for the entire journey. We need to find the speed of the current, given that the boat's own speed is 20 km/h.

Solution

Let's assume the speed of the 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. So, the effective 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. So, the effective 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 18 / (20 + x) hours.

The time taken to travel upstream is given by 20 / (20 - x) hours.

According to the problem, the total time taken for the entire journey is 2 hours. So, we can write the equation:

18 / (20 + x) + 20 / (20 - x) = 2

To solve this equation, we can multiply through by the denominators to get rid of the fractions:

18(20 - x) + 20(20 + x) = 2(20 + x)(20 - x)

Simplifying this equation will give us the value of x, which represents the speed of the current.

Let's solve the equation step by step:

18(20 - x) + 20(20 + x) = 2(20 + x)(20 - x)

Expanding the equation:

360 - 18x + 400 + 20x = 2(400 - x^2)

Combining like terms:

760 + 2x = 800 - 2x^2

Rearranging the equation:

2x^2 + 2x - 40 = 0

Dividing through by 2:

x^2 + x - 20 = 0

Factoring the quadratic equation:

(x + 5)(x - 4) = 0

Setting each factor equal to zero:

x + 5 = 0 or x - 4 = 0

Solving for x:

x = -5 or x = 4

Since the speed of the current cannot be negative, we discard the solution x = -5.

Therefore, the speed of the current is 4 km/h.

Answer

The speed of the current is 4 km/h.