Question

Пассажирский катер проходит расстояние 150 км по течению реки за 2 ч,а против течения за 3 ч.Найти скорость катера в стоячей воде.Ответ:62,5 км/ч.

Answer 1

S=150 км    t1=2 ч    t2=3 ч     vk=?
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vk+vp=s/t1
vk-vp=s/t2
2*vk=s*(1/t1+1/t2)
vk=s*(1/t1+1/t2)/2=150*(1/2+1/3)/2=62.5 км/ч
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Answer 2

Problem Analysis

We are given that a passenger boat travels a distance of 150 km downstream in 2 hours and the same distance upstream in 3 hours. We need to find the speed of the boat in still water.

Downstream Speed Calculation

Let's assume the speed of the boat in still water is x km/h, and the speed of the river current is y km/h. When the boat is traveling downstream, it will benefit from the speed of the river current, so its effective speed will be (x + y) km/h.

We are given that the boat travels a distance of 150 km downstream in 2 hours. Using the formula distance = speed × time, we can write the equation:

150 = (x + y) × 2

Upstream Speed Calculation

When the boat is traveling upstream, it will be working against the speed of the river current, so its effective speed will be (x - y) km/h.

We are given that the boat travels a distance of 150 km upstream in 3 hours. Using the same formula as before, we can write the equation:

150 = (x - y) × 3

Solving the Equations

We now have a system of two equations with two variables. We can solve this system to find the values of x and y.

Let's solve the equations:

From equation 1: 150 = (x + y) × 2 From equation 2: 150 = (x - y) × 3

Expanding the equations:

300 = 2x + 2y 450 = 3x - 3y

Rearranging the equations:

2x + 2y = 300 3x - 3y = 450

We can solve this system of equations using the method of elimination. Multiplying the first equation by 3 and the second equation by 2, we get:

6x + 6y = 900 6x - 6y = 900

Adding the two equations together, we eliminate the variable y:

12x = 1800

Dividing both sides by 12, we find:

x = 150

Finding the Speed of the Boat in Still Water

We have found that the speed of the boat in still water (x) is 150 km/h.

Answer

The speed of the boat in still water is 150 km/h.