Question

Лодка 30 км проходит за 3 часа по течению реки и 28 км за 4 часа против течения. Найдите скорость течения реки и собственную скорость теплохода.

Answer 1

Допустим x-скорость реки, а y - скорость теплохода, тогда $\frac{30}{3}=x+y$, и $\frac{28}{4}=y-x$, следовательно скорсть течения ровна 1.5 а скорость теплохода 8.5

Answer 2

Собственная скорость лодки Х км/ч  Скорость течения реки У км/ч  Скорость лодки по течению (Х + У) км. ч Скорость лодки против течения (Х - У) км/ч   (Х + У) * 3 1/3 = 30 (X - У) *4 = 28  Реши систему из двух уравненеий, найди Х. Это скорость лодки по озеру. У * 1,5 = расстояние, которое пройдет лодка по озеру
как то так

Answer 3

Problem Analysis

We are given that a boat travels 30 km downstream in 3 hours and 28 km upstream in 4 hours. We need to find the speed of the river's current and the speed of the boat.

Downstream Speed Calculation

Let's assume the speed of the boat in still water is B km/h and the speed of the river's current is C km/h. When the boat is traveling downstream, the effective speed is the sum of the boat's speed and the current's speed. Therefore, the boat's speed downstream is B + C km/h.

We are given that the boat travels 30 km downstream in 3 hours. Using the formula speed = distance / time, we can write the equation:

B + C = 30 / 3

Upstream Speed Calculation

When the boat is traveling upstream, the effective speed is the difference between the boat's speed and the current's speed. Therefore, the boat's speed upstream is B - C km/h.

We are given that the boat travels 28 km upstream in 4 hours. Using the formula speed = distance / time, we can write the equation:

B - C = 28 / 4

Solving the Equations

We now have a system of equations:

B + C = 10 (Equation 1) B - C = 7 (Equation 2)

We can solve this system of equations to find the values of B and C.

Adding Equation 1 and Equation 2, we get:

(B + C) + (B - C) = 10 + 7 2B = 17 B = 17 / 2 B = 8.5

Substituting the value of B into Equation 1, we get:

8.5 + C = 10 C = 10 - 8.5 C = 1.5

Answer

The speed of the river's current is 1.5 km/h and the speed of the boat in still water is 8.5 km/h.

Please note that the above calculations are based on the given information and assumptions.