Question

От двух пристаней на реке движутся навстречу друг другу два катера, собственные скорости которых равны. До встречи, катер, идущий по течению, шёл 1 час 6 минут; а катер, идущий против течения, 1,5 часа. Катер, идущий по течению, до встречи прошёл на 1 км больше другого катера. Найдите собственную скорость каждого катера, если скорость течения 3 км/ч. ПОМОГИТЕ ПОЖАЛУЙСТА!!!!!!!!!!!​

Answer 1

скорость катера, движущегося по течению,  состоит из скорости собственной и скорости течения реки, т.е. если его собст. скорость х,  то по течению (х+3), тогда до встречи этот катер проплыл 1 6/60 часа , т.е. 1.1 часа, 1.1*(х+3) км, а второй катер 1.5*(х-3) км до встречи, т.к. плыл против течения. скорость течения вычли из собственной скорости катера.

разность составила 1 км, отсюда уравнение

1.1*(х+3)-1.5*(х-3) =1

1.1х+3.3-1.5х+4.5 =1

6.8=0.4х

х=68/4

х=17

Значит, собственная скорость каждого катера 17 км/ч, т.к. их скорости собственные равны.

Ответ  17 км/ч,  17км/ч

Answer 2

Ответ:

17 КМ/ЧАС

Пошаговое объяснение:

х скорость катера

1,5*(х -3)-1,1* (х+3)=1

1,5х-4,5-1,1х-3,3=1

0,4х=7,8-1=6,8

х=17 собственная скорость катера

проверка:

1,1 (17+3)-1,5*(17-3)-=1,1*20-1,5*14=22-21=1

1=1

Answer 3

Problem Analysis

We are given two boats moving towards each other on a river. The boats have the same speed, and one boat is moving with the current while the other is moving against the current. We are also given the time it took for each boat to reach the meeting point and the distance traveled by the boat moving with the current. We need to find the speed of each boat.

Solution

Let's denote the speed of each boat as x km/h. Since both boats have the same speed, the speed of the boat moving against the current will be x - 3 km/h (subtracting the speed of the current), and the speed of the boat moving with the current will be x + 3 km/h (adding the speed of the current).

We are given that the boat moving with the current traveled 1 km more than the other boat. Let's denote the distance traveled by the boat moving against the current as d km. Therefore, the distance traveled by the boat moving with the current will be d + 1 km.

We can use the formula speed = distance / time to find the speed of each boat.

For the boat moving with the current: x + 3 = (d + 1) / (1 hour + 6 minutes)

For the boat moving against the current: x - 3 = d / (1 hour + 30 minutes)

To solve this system of equations, we can use substitution or elimination.

Solution using Substitution

We can solve the second equation for d and substitute it into the first equation.

From the second equation: d = (x - 3) * (1 hour + 30 minutes)

Substituting this into the first equation: x + 3 = [(x - 3) * (1 hour + 30 minutes) + 1] / (1 hour + 6 minutes)

Simplifying the equation: x + 3 = [(x - 3) * (90 minutes) + 1] / (66 minutes)

Now we can solve this equation to find the value of x.

Let's calculate the solution.

Calculation

Using the equation: x + 3 = [(x - 3) * (90 minutes) + 1] / (66 minutes)

We can cross-multiply to eliminate the denominators: 66 minutes * (x + 3) = (x - 3) * (90 minutes) + 1

Simplifying the equation: 66x + 198 = 90x - 270 + 1

Combining like terms: 66x + 198 = 90x - 269

Moving all the terms to one side: 24x = 467

Dividing both sides by 24: x = 19.4583

Therefore, the speed of each boat is approximately 19.4583 km/h.

Answer

The speed of each boat is approximately 19.4583 km/h.