Question

Расстояние между двумя пританямя по реке равно 80 км. Это растояние катер проплывает по течению за 4 ч, против течение за 5 ч. Найдите собственую скорость катера и скорость течение реки.

Answer 1

Скорость катера по течению : 80 / 4 = 20 км/ч = скорость катера + течение
Скорость катера против течения : 80 / 5 = 16 км/ч = скорость катера - течение
Скорость течения равна : (20 - 16) / 2 = 2 км/ч
Собственная скорость катера : 16 + 2 = 18 км/ч

Answer 2

Problem Analysis

We are given the following information: - The distance between two points along a river is 80 km. - A boat can travel downstream (with the current) in 4 hours. - The same boat can travel upstream (against the current) in 5 hours.

We need to find the speed of the boat and the speed of the river current.

Downstream Speed Calculation

Let's assume the speed of the boat is B km/h and the speed of the river current is C km/h. When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river current. Therefore, the boat's effective speed downstream is (B + C) km/h.

Using the formula speed = distance / time, we can calculate the effective speed downstream: - Distance = 80 km - Time = 4 hours

So, we have the equation: (B + C) = 80 / 4.

Upstream Speed Calculation

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current. Therefore, the boat's effective speed upstream is (B - C) km/h.

Using the formula speed = distance / time, we can calculate the effective speed upstream: - Distance = 80 km - Time = 5 hours

So, we have the equation: (B - C) = 80 / 5.

Solving the Equations

We now have a system of two equations with two unknowns: 1. (B + C) = 80 / 4 2. (B - C) = 80 / 5

We can solve this system of equations to find the values of B and C.

Solution

Let's solve the system of equations:

Equation 1: (B + C) = 80 / 4

Equation 2: (B - C) = 80 / 5

Adding Equation 1 and Equation 2, we get:

(B + C) + (B - C) = 80 / 4 + 80 / 5

Simplifying the equation, we have:

2B = 20 + 16

2B = 36

Dividing both sides by 2, we get:

B = 18

Substituting the value of B into Equation 1, we have:

(18 + C) = 80 / 4

Simplifying the equation, we have:

18 + C = 20

Subtracting 18 from both sides, we get:

C = 2

Therefore, the speed of the boat is 18 km/h and the speed of the river current is 2 km/h.

Answer

The speed of the boat is 18 km/h and the speed of the river current is 2 km/h.