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

S = v * t - формула пути
1 ч 20 мин = 1  целая 1/3 ч = 4/3 ч
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1) 24 : 4/3 = 24 * 3/4 = 6 * 3 = 18 (км/ч) - скорость катера по течению реки;
2) 18 - 3 = 15 (км) - расстояние, которое проплыл катер против течения реки;
3) 15 : 1,5 = 10 (км/ч) - скорость катера против течения реки;
4) (18 - 10) : 2 = 4 (км/ч) - скорость течения реки;
5) 18 - 4 = 10 + 4 = 14 (км/ч) - собственная скорость катера.
Ответ: 4 км/ч; 14 км/ч.

Answer 2

Problem Analysis

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

Solution

Let's assume the speed of the boat is x km/h and the speed of the current is v km/h.

When the boat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's effective speed is (x + v) km/h.

According to the given information, the boat travels 24 km in 1 hour and 20 minutes (which is 1.33 hours) with the current. Using the formula distance = speed × time, we can write the equation:

(x + v) × 1.33 = 24 When the boat is traveling against the current, its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's effective speed is (x - v) km/h.

According to the given information, the boat travels 3 km less in 1 hour and 30 minutes (which is 1.5 hours) against the current compared to its speed with the current. Using the formula distance = speed × time, we can write the equation:

(x - v) × 1.5 = 24 - 3 Now we have a system of two equations with two variables. We can solve this system to find the values of x and v.

Solving the System of Equations

Let's solve the system of equations and to find the values of x and v.

From equation (x + v) × 1.33 = 24

Expanding the equation: 1.33x + 1.33v = 24

From equation (x - v) × 1.5 = 21

Expanding the equation: 1.5x - 1.5v = 21

Now we have a system of linear equations: 1.33x + 1.33v = 24 1.5x - 1.5v = 21 To solve this system, we can use the method of elimination. Let's multiply equation by 1.5 and equation by 1.33 to eliminate the variable v.

Multiplying equation by 1.5: 1.5 × (1.33x + 1.33v) = 1.5 × 24 1.995x + 1.995v = 36 Multiplying equation by 1.33: 1.33 × (1.5x - 1.5v) = 1.33 × 21 1.995x - 1.995v = 27.93 Now we have a new system of equations: 1.995x + 1.995v = 36 1.995x - 1.995v = 27.93 Adding equations and eliminates the variable v: (1.995x + 1.995v) + (1.995x - 1.995v) = 36 + 27.93 3.99x = 63.93

Simplifying: 3.99x = 63.93

Dividing both sides by 3.99: x = 63.93 / 3.99 x ≈ 16

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of v.

Using equation (x + v) × 1.33 = 24

Substituting x = 16: (16 + v) × 1.33 = 24

Expanding and simplifying: 21.28 + 1.33v = 24

Subtracting 21.28 from both sides: 1.33v = 2.72

Dividing both sides by 1.33: v ≈ 2.05

Therefore, the speed of the current is approximately 2.05 km/h and the speed of the boat is approximately 16 km/h.

Answer

The speed of the current is approximately 2.05 km/h and the speed of the boat is approximately 16 km/h.