Question

Катер прошёл по течению реки от пристани А до пристани В и вернулся назад. Скорость течения реки 3км/ч.Найдите скорость катера в стоячей воде, если: а) от А до В катер шел 1,5ч,а от В до А-2ч; б)скорость катера против течения реки составляет 75% скорости по течению.

Answer 1

 

Пусть собственная скорость катера х км/ч
Тогда по течению он плыл со скоростью х+3 км/ч
а против течения х-3 км/ч

 Расстояние от А до В и от В до А одинаково.

(х-3)=0,75*(х+3)

Составим уравнение. 

(х+3)*1,5 =(х-3)2

1,5х+4,5=2х-6
0,5х=10,5
х=21 км/ч

х+3=24 скорость по течению
х-3=18 скорость против течения
Проверка:
24*0,75=18

 

Собственная скорость катера 21 км/ч

Answer 2

Problem Analysis

We are given that a boat traveled from point A to point B and then returned from point B to point A. The speed of the river current is 3 km/h. We need to find the speed of the boat in still water under two different scenarios: a) The boat took 1.5 hours to travel from A to B and 2 hours to return from B to A. b) The speed of the boat against the current is 75% of the speed of the boat with the current.

Solution

a) To find the speed of the boat in still water, we can use the formula: speed of boat in still water = (distance traveled) / (time taken).

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

From A to B: - Distance = x km/h * 1.5 hours - Time = 1.5 hours

From B to A: - Distance = x km/h * 2 hours - Time = 2 hours

Since the boat is traveling with the current from A to B and against the current from B to A, the effective speed of the boat will be reduced by the speed of the current when traveling against it.

From A to B, the effective speed of the boat is (x + 3) km/h (since it is traveling with the current).

From B to A, the effective speed of the boat is (x - 3) km/h (since it is traveling against the current).

Using the formula, we can set up the following equations:

1.5 = (x + 3) km/h * 1.5 hours 2 = (x - 3) km/h * 2 hours Now, let's solve these equations to find the value of x.

b) To find the speed of the boat in still water when traveling against the current, we can use the formula: speed of boat in still water = (speed of boat with current) / (1 + (speed of current / speed of boat against current)).

Let's assume the speed of the boat with the current is y km/h.

The speed of the boat against the current is 75% of the speed of the boat with the current, so the speed of the boat against the current is 0.75y km/h.

Using the formula, we can set up the following equation:

x = y / (1 + (0.75y / 3)) Now, let's solve this equation to find the value of x.

Solution Steps

a) To find the speed of the boat in still water when given the time taken for each leg of the journey: 1. Set up the equations using the distances and times given. 2. Solve the equations to find the value of x.

b) To find the speed of the boat in still water when given the speed of the boat with the current: 1. Set up the equation using the given information. 2. Solve the equation to find the value of x.

Solution for Part a)

Let's solve the equations from step 1 to find the value of x.

From equation 1.5 = (x + 3) km/h * 1.5 hours

Simplifying the equation: 1.5 = 1.5x + 4.5

Subtracting 4.5 from both sides: 1.5 - 4.5 = 1.5x

-3 = 1.5x

Dividing both sides by 1.5: x = -2

From equation 2 = (x - 3) km/h * 2 hours

Simplifying the equation: 2 = 2x - 6

Adding 6 to both sides: 2 + 6 = 2x

8 = 2x

Dividing both sides by 2: x = 4

Therefore, the speed of the boat in still water is 4 km/h.

Solution for Part b)

Let's solve the equation from step 1 to find the value of x.

From equation x = y / (1 + (0.75y / 3))

Simplifying the equation: x = y / (1 + 0.25y)

Multiplying both sides by (1 + 0.25y): x(1 + 0.25y) = y

Expanding the equation: x + 0.25xy = y

Subtracting 0.25xy from both sides: x = y - 0.25xy

Factoring out x on the right side: x = y(1 - 0.25x)

Dividing both sides by (1 - 0.25x): x / (1 - 0.25x) = y

Therefore, the speed of the boat in still water is x / (1 - 0.25x).

Summary

a) The speed of the boat in still water is 4 km/h when it took 1.5 hours to travel from A to B and 2 hours to return from B to A.

b) The speed of the boat in still water is x / (1 - 0.25x) when the speed of the boat with the current is y km/h and the speed of the boat against the current is 75% of the speed of the boat with the current.

Please note that the values of y and x were not provided in the question, so we cannot calculate the exact speed of the boat in still water in this scenario without additional information.