Question

Катер проплыв 158 км, плыл 1.5 часа по течению и 2.5 часа против течения. Скорость течения реки 2 км час. Найти собственную скорость катера и расстояние, которое он проплыл по течению реки

Answer 1

Пусть скорость течения катера будет равна х
тогда скорость течения катера по течению равна х+2
а против течения х-2
расстояние пройденное по течению равно (х+2)1.5
расстояние пройденное против течения равно (х-2)2.5
зная что всего катер проплыл 158км составим уравнение
1.5(х+2)+2.5(х-2)=158
1.5+3+2.5х-5=158
4х=160
х=160:4=40км/ч собственная скорость катера
расстояние пройденное по течению равно (х+2)1.5=(40+2)1.5=63км

Answer 2

Problem Analysis

We are given the following information: - The boat traveled a distance of 158 km. - It traveled for 1.5 hours with the current. - It traveled for 2.5 hours against the current. - The speed of the current is 2 km/h.

We need to find: - The speed of the boat in still water. - The distance traveled by the boat with the current.

Calculating the Speed of the Boat in Still Water

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

When the boat is traveling with the current, its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed is (x + 2) km/h.

When the boat is traveling against the current, its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed is (x - 2) km/h.

Calculating the Distance Traveled with the Current

The formula to calculate distance is speed × time.

When the boat is traveling with the current, the distance traveled is (x + 2) × 1.5 km.

When the boat is traveling against the current, the distance traveled is (x - 2) × 2.5 km.

Solving the Equations

We can set up two equations based on the information given and solve them to find the values of x and the distance traveled with the current.

Equation 1: Distance traveled with the current = 158 km Equation 2: Distance traveled with the current = (x + 2) × 1.5 km

By equating the two equations, we can solve for x.

Let's solve the equations to find the values.

Solution

Let's solve the equations to find the values of x and the distance traveled with the current.

Equation 1: Distance traveled with the current = 158 km Equation 2: Distance traveled with the current = (x + 2) × 1.5 km

Setting the two equations equal to each other: (x + 2) × 1.5 = 158

Simplifying the equation: 1.5x + 3 = 158 1.5x = 155 x = 155 / 1.5 x ≈ 103.33

Therefore, the speed of the boat in still water is approximately 103.33 km/h.

To find the distance traveled with the current, we can substitute the value of x into Equation 2: Distance traveled with the current = (103.33 + 2) × 1.5 Distance traveled with the current ≈ 157.99 km

Therefore, the distance traveled by the boat with the current is approximately 157.99 km.

Answer

The speed of the boat in still water is approximately 103.33 km/h and the distance it traveled with the current is approximately 157.99 km.