Question

Катер за 1 ч 20 мин проплывает по течению реки 24 км,а против течения за 1,5 ч на 3 км меньше .найдите скорость течения реки и собственную скорость катера .

Answer 1

1ч20м=1 20/60=1 1/3=4/3ч
24-3=21
х-собств.скорость
у-скорость течения
24:4/3=х+у
21:1,5=х-у

24*3/4=х+у
18=х+у
14=х-у

х=18-у

14=18-у-у
2у=4
у=2-скорость течения
х=18-2=16-собств.скорость

Answer 2

Problem Analysis

We are given that a boat travels 24 km downstream in 1 hour and 20 minutes, and it travels 3 km less upstream in 1 hour and 30 minutes. We need to find the speed of the river current and the speed of the boat.

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 benefits from the speed of the river current, so its effective speed is x + y km/h. We can use this information to set up the following equation:

24 = (x + y) × (1 + 20/60)

Upstream Speed Calculation

When the boat is traveling upstream, it has to overcome the speed of the river current, so its effective speed is x - y km/h. We can use this information to set up the following equation:

24 - 3 = (x - y) × (1 + 30/60)

Solving the Equations

We can solve these two equations simultaneously to find the values of x and y.

Solution

Let's solve the equations to find the speed of the river current and the speed of the boat.

Solution Details

Using the given information, we can set up the following equations:

24 = (x + y) × (1 + 20/60) (Equation 1)

24 - 3 = (x - y) × (1 + 30/60) (Equation 2)

Simplifying Equation 1:

24 = (x + y) × (1.3333)

24 = 1.3333x + 1.3333y

Simplifying Equation 2:

21 = (x - y) × (1.5)

21 = 1.5x - 1.5y

Now we have a system of linear equations:

1.3333x + 1.3333y = 24 (Equation 3)

1.5x - 1.5y = 21 (Equation 4)

We can solve this system of equations using any method, such as substitution or elimination. Let's use the elimination method to solve for x and y.

Multiplying Equation 3 by 1.5 and Equation 4 by 1.3333 to eliminate the y term:

1.99995x + 1.99995y = 36 (Equation 5)

1.99995x - 1.99995y = 28 (Equation 6)

Subtracting Equation 6 from Equation 5 to eliminate the x term:

3.9999y = 8

y = 8 / 3.9999

y ≈ 2

Substituting the value of y into Equation 3:

1.3333x + 1.3333(2) = 24

1.3333x + 2.6666 = 24

1.3333x = 21.3334

x = 21.3334 / 1.3333

x ≈ 16

Therefore, the speed of the river current is approximately 2 km/h and the speed of the boat in still water is approximately 16 km/h.

Answer

The speed of the river current is approximately 2 km/h and the speed of the boat in still water is approximately 16 km/h.