Question

Моторная лодка за 3,5 ч проплыла 43,4 км по точению реки и за 4,5 ч проплыла 39,6 км против течения.Найдите собственную скорость лодки и скорость течения. СРООООООЧНО ПОЖАЙЛУСТА))

Answer 1

43,4/3,5-скорость по течению 12,4км/час
39,6/3,5-скорость против течения 8,8км/час
12,4-8,8=3,6км/час-скорость течения

Answer 2

Calculation of Boat's Speed and Current Speed

To find the boat's speed and the speed of the current, we can use the formula:

Distance = Speed x Time

Let's denote the boat's speed as B and the speed of the current as C.

1. When the boat is moving downstream (with the current), it covers a distance of 43.4 km in 3.5 hours. Using the formula, we have:

43.4 = (B + C) x 3.5 2. When the boat is moving upstream (against the current), it covers a distance of 39.6 km in 4.5 hours. Using the formula, we have:

39.6 = (B - C) x 4.5 Now, we have a system of two equations with two unknowns (B and C). We can solve this system of equations to find the values of B and C.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation 1, we can express B in terms of C:

B = (43.4 / 3.5) - C

Substituting this value of B into equation 2, we get:

(43.4 / 3.5 - C) - C = 39.6 / 4.5

Simplifying the equation:

(43.4 / 3.5) - 2C = 39.6 / 4.5

Now, we can solve this equation to find the value of C.

Calculation

Let's calculate the value of C using the equation:

(43.4 / 3.5) - 2C = 39.6 / 4.5

Simplifying the equation:

(43.4 / 3.5) - 2C = 8.8

Multiplying both sides by 3.5 to eliminate the denominator:

43.4 - 7C = 30.8

Rearranging the equation:

7C = 43.4 - 30.8

7C = 12.6

Dividing both sides by 7:

C = 12.6 / 7

C ≈ 1.8 km/h

Now that we have the value of C, we can substitute it back into equation 1 to find the value of B.

Using equation 1:

43.4 = (B + 1.8) x 3.5

Simplifying the equation:

43.4 = 3.5B + 6.3

Subtracting 6.3 from both sides:

43.4 - 6.3 = 3.5B

37.1 = 3.5B

Dividing both sides by 3.5:

B = 37.1 / 3.5

B ≈ 10.6 km/h

Answer

The boat's speed is approximately 10.6 km/h and the speed of the current is approximately 1.8 km/h.