Question

Катер прошел по течению 120км. На этот же путь против течения он тратит в 1,5 раза больше. Найдите скорость течения если скорость катера в стоячей воде 20км/ч. ПОМОГИТЕ БЫСТРЕЕ ПОЖАЛУЙСТА!!!

Answer 1

Пусть скорость течения х км/ ч,

Тогда скорость по течению (20+х) км/ ч,

а скорость против течения (20-х) км/ ч.

Время по течению 120/(20+х) ч,

время против течения 120/(20-х) ч.

Тк на путь против течения он тратит в 1,5 раза больше, то составим уравнение

120/(20-х) =120/(20+х)*1,5 |*(20-х) (20+х),

120*(20+х) =1,5*120*(20-х) ,

20+х =1,5*(20-х)

х+1,5х=1, 5*20-20

2,5х=10

х=4

Скорость течения реки 4 км/ ч.

Answer 2

Problem Analysis

We are given that a boat travels a distance of 120 km downstream and takes 1.5 times longer to cover the same distance upstream. We need to find the speed of the current if the speed of the boat in still water is 20 km/h.

Downstream Speed

Let's assume the speed of the current is c km/h. When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the downstream speed is 20 + c km/h.

Upstream Speed

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the upstream speed is 20 - c km/h.

Time Ratio

We are given that the boat takes 1.5 times longer to cover the same distance upstream compared to downstream. This means that the time taken to travel upstream is 1.5 times the time taken to travel downstream.

Let's calculate the time taken to travel downstream and upstream using the formula time = distance / speed.

Time Downstream

The time taken to travel downstream is given by 120 / (20 + c) hours.

Time Upstream

The time taken to travel upstream is given by 120 / (20 - c) hours.

Time Ratio Equation

We can set up the equation (120 / (20 - c)) = 1.5 * (120 / (20 + c)) to represent the time ratio.

Solving the Equation

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

(120 / (20 - c)) = 1.5 * (120 / (20 + c))  # Multiply both sides by (20 - c) and (20 + c)
120 * (20 + c) = 1.5 * 120 * (20 - c)      # Cancel out the common factors
20 + c = 1.5 * (20 - c)                    # Simplify
20 + c = 30 - 1.5c                          # Distribute 1.5
2.5c = 10                                  # Combine like terms
c = 4                                      # Divide both sides by 2.5

Answer

The speed of the current is 4 km/h.

Verification

Let's verify the answer by substituting the value of c into the equation and checking if both sides are equal.

(120 / (20 - 4)) = 1.5 * (120 / (20 + 4))
(120 / 16) = 1.5 * (120 / 24)
7.5 = 1.5 * 5
7.5 = 7.5

The equation holds true, which confirms that the speed of the current is indeed 4 km/h.