Question

Помогите решить С:Катер в 11:00 вышел из пункта А в пункт В, расположенный в 15 км от А. Пробыв в пункте В 1 час 20 минут, катер отправился назад и вернулся обратно впункт А в 15:00 того же дня. Определите (в км/ч) собственную скорость катера, если известно, что скорость течения реки равна 3 км/ч.

Answer 1

Х- собственная скорость
(х+3)- скорость катера по течению
(х-3) - скорость катера против течения
4 часа - всего в пути был катер (с 11.00 до 15,00)
1ч 20 мин или 1 1/3 длилась остановка, тогда можем узнать сколько катер находился на плаву, т. е передвигалась:
4-1 1/3= 2 2/3 или 2часа 40 мин - это время плавания
Зная, что путь в один конец 15 км, составим уравнение:
15:(х+3)+15:(х-3)=2 2/3
Решаем уравнение и получаем ответ - значение х - собственная скорость катера))) как-то так...

Answer 2

Problem Analysis

We are given the following information: - A boat departs from point A to point B at 11:00. - Point B is located 15 km away from point A. - The boat stays at point B for 1 hour and 20 minutes. - The boat returns to point A and arrives at 15:00 on the same day. - The speed of the river current is 3 km/h.

We need to determine the speed of the boat.

Solution

To solve this problem, we can use the formula: distance = speed × time.

Let's break down the problem into two parts: the journey from point A to point B and the journey from point B back to point A.

# Journey from Point A to Point B

Let's assume the speed of the boat is x km/h.

The distance from point A to point B is 15 km.

The time taken to travel from point A to point B can be calculated using the formula: time = distance / speed.

Substituting the values, we have: 15 km = x km/h × time.

# Journey from Point B to Point A

On the return journey, the boat is traveling against the current of the river. The speed of the current is given as 3 km/h.

The effective speed of the boat against the current will be (x - 3) km/h.

The distance from point B to point A is also 15 km.

The time taken to travel from point B to point A can be calculated using the formula: time = distance / speed.

Substituting the values, we have: 15 km = (x - 3) km/h × time.

# Total Time

The total time taken for the entire journey is given as 3 hours and 20 minutes, which is equivalent to 3.33 hours.

The total time is the sum of the time taken for the journey from point A to point B and the journey from point B to point A.

So, we have: time + time = 3.33 hours.

# Solving the Equations

We have two equations: 1. 15 km = x km/h × time 2. 15 km = (x - 3) km/h × time

We also have the equation: time + time = 3.33 hours.

We can solve these equations simultaneously to find the value of x, which represents the speed of the boat.

Calculation

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

From equation 1, we have: 15 km = x km/h × time.

From equation 2, we have: 15 km = (x - 3) km/h × time.

We can rewrite equation 2 as: 15 km = (x - 3) km/h × (3.33 hours - time).

Substituting equation 1 into equation 2, we have: 15 km = (x - 3) km/h × (3.33 hours - (15 km / x km/h)).

Simplifying the equation, we get: 15 km = (x - 3) km/h × (3.33 hours - (15 / x) hours).

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

Answer

The speed of the boat is approximately 12.5 km/h.

Please note that the above calculation is based on the given information and assumptions made.