Question

Расстояние между двумя пристанями по реке равно 27 км. Катер проплывает его по течению реки за 1,5 ч, а против течения за 2 ч 15 м. Найти собственную скорость катера и скорость течения реки.

Answer 1

1)  V1 + V2 = 27 : 1.5 = 18 км/ч - скорость по течению
2 ч 15 мин = 2,25 ч - перевели минуты в часы.
2) V1 - V2 = 27 : 2.25 = 12 км/ч - скорость против течения.
Сложили уравнения -  1) + 2 = 3 и получили
3)  2*V1 = 18 + 12 = 30 или
V1 = 30 : 2 = 15 км/ч -  скорость катера - ОТВЕТ
Вычитаем уравнения - 1) - 2) = 4)
4)  2*V2 = 18 - 12 = 6 или
V2 = 6:2 = 3 км/ч - скорость течения - ОТВЕТ

Answer 2

Problem Analysis

We are given that the distance between two piers on a river is 27 km. The boat can travel downstream in 1.5 hours and upstream in 2 hours and 15 minutes. We need to find the speed of the boat and the speed of the river current.

Downstream Speed Calculation

To find the speed of the boat, we can use the formula: distance = speed × time. When the boat is traveling downstream, it is assisted by the river current, so the effective speed of the boat is the sum of its own speed and the speed of the river current. Let's assume the speed of the boat is B and the speed of the river current is C. The distance traveled downstream is 27 km, and the time taken is 1.5 hours. Therefore, we can write the equation as: 27 = (B + C) × 1.5.

Upstream Speed Calculation

When the boat is traveling upstream, it is going against the river current, so the effective speed of the boat is the difference between its own speed and the speed of the river current. Using the same assumptions as before, we can write the equation for the upstream journey as: 27 = (B - C) × (2 + 15/60).

Solving the Equations

We now have two equations with two unknowns (B and C). We can solve these equations simultaneously to find the values of B and C.

Solution

Let's solve the equations to find the speed of the boat (B) and the speed of the river current (C).

From the first equation, we have: 27 = (B + C) × 1.5. (Equation 1)

From the second equation, we have: 27 = (B - C) × (2 + 15/60). (Equation 2)

To simplify Equation 2, we can convert 2 hours and 15 minutes to hours: 2 hours + 15 minutes = 2 + 15/60 = 2.25 hours.

Now, let's substitute the values into the equations and solve them simultaneously.

Solution Steps:

1. Equation 1: 27 = (B + C) × 1.5 2. Equation 2: 27 = (B - C) × 2.25

Let's solve these equations to find the values of B and C.

Solution:

1. Equation 1: 27 = (B + C) × 1.5 2. Equation 2: 27 = (B - C) × 2.25

To solve these equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From Equation 1, we can express B in terms of C: B = 27/1.5 - C.

Substituting this value of B into Equation 2, we get: 27 = (27/1.5 - C - C) × 2.25.

Simplifying the equation: 27 = (18 - 2C) × 2.25.

Expanding and rearranging the equation: 27 = 40.5 - 4.5C.

Bringing all the terms to one side: 4.5C = 40.5 - 27.

Simplifying: 4.5C = 13.5.

Dividing both sides by 4.5: C = 13.5/4.5.

Calculating: C = 3.

Now that we have the value of C, we can substitute it back into Equation 1 to find B: 27 = (B + 3) × 1.5.

Expanding and rearranging the equation: 27 = 1.5B + 4.5.

Bringing all the terms to one side: 1.5B = 27 - 4.5.

Simplifying: 1.5B = 22.5.

Dividing both sides by 1.5: B = 22.5/1.5.

Calculating: B = 15.

Therefore, the speed of the boat (B) is 15 km/h and the speed of the river current (C) is 3 km/h.

Answer

The speed of the boat is 15 km/h and the speed of the river current is 3 km/h.