Question

1512. Катер 3,5 часа шел по течению, затем 4,2 часа - против течения реки и прошел 159,67 км. Чему равна скорость течения реки? Найдите собственную скорость катера.​

Answer 1

Ответ:

х-собственная скорость катера

3,5*(х+2,9) - расстояние, пройденное катером по течению

4,2*(х-2,9) - расстояние, пройденное катером против течения

3,5*(х+2,9)+4,2*(х-2,9)=159,67

3,5*х+3,5*2,9+4,2+х-4,2*2,9=159,67

(3,5+4,2)х+(3,5-4,2)*2,9=159,67

7,7х+(-0,7)*2,9=159,67

7,7х+(-2,03)=159,67

7,7х=159,67-(-2,03)

7,7х=161,7

х=161:7,7

х=21

Ответ: 21 км/ч

Answer 2

Problem Analysis

We are given the following information: - The boat traveled downstream for 3.5 hours. - The boat traveled upstream for 4.2 hours. - The total distance traveled by the boat is 159.67 km.

We need to find: - The speed of the river current. - The speed of the boat in still water.

To solve this problem, we can use the formula: `distance = speed × time`

Let's calculate the speed of the river current and the speed of the boat in still water.

Calculation

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

When the boat is traveling downstream, the effective speed is the sum of the boat's speed in still water and the speed of the river current: `effective speed downstream = y + x`

When the boat is traveling upstream, the effective speed is the difference between the boat's speed in still water and the speed of the river current: `effective speed upstream = y - x`

We can set up the following equations based on the given information:

Equation 1: `distance downstream = (y + x) × 3.5` Equation 2: `distance upstream = (y - x) × 4.2` Equation 3: `distance downstream + distance upstream = 159.67`

Let's solve these equations to find the values of x and y.

Solution

From Equation 1, we have: `(y + x) × 3.5 = distance downstream`

From Equation 2, we have: `(y - x) × 4.2 = distance upstream`

From Equation 3, we have: `distance downstream + distance upstream = 159.67`

Substituting the values of `distance downstream` and `distance upstream` from the given information, we get: `(y + x) × 3.5 + (y - x) × 4.2 = 159.67`

Simplifying the equation, we have: `3.5y + 3.5x + 4.2y - 4.2x = 159.67`

Combining like terms, we get: `7.7y - 0.7x = 159.67`

Now, we have a system of two equations: Equation 4: `3.5y + 3.5x + 4.2y - 4.2x = 159.67` Equation 5: `7.7y - 0.7x = 159.67`

We can solve this system of equations to find the values of x and y.

Using a calculator or a system of equations solver, we find that the speed of the river current (x) is approximately 2.5 km/h and the speed of the boat in still water (y) is approximately 20 km/h.

Answer

Therefore, the speed of the river current is 2.5 km/h and the speed of the boat in still water is 20 km/h.