Question

4. Катер за 3.5 часа по озеру и за 2 часа против течения реки проплывает такое же расстоя- ние, что за 2,5 ч по течению реки. Найдите собственную скорость катера, если скорость течения реки равна 4 км/ч.​

Answer 1

Ответ:

Собственная скорость катера равна 6км/ч.

Формула:

$v = \frac{l}{t}$

*где v - скорость, l - расстояние, t - время.

Решение:

Пусть собственная скорость катера будет х км/ч.

• В озере скорость течения равна нулю, поэтому по озеру катер перемещался со скоростью х км/ч. За 3.5 часа по озеру проплыл 3,5х км.
• Против течения реки катер перемещается со скоростью (х-4)км/ч. За два часа проплывает 2(х-4)км.
• По течению реки катер перемещается со скоростью (х+4)км/ч. За 2.5 часа проплывает 2.5(х+4)км.

Расстояние, которое проплывает катер за 3,5 часа по озеру и 2 часа против течения, равно расстоянию, которое он проплывает за 2.5 часа по течению. Имеем уравнение:

$3.5x + 2(x - 4) = 2.5(x + 4) \\ \\ 3.5x + 2x - 8 = 2.5x + 10 \\ \\ 5.5x - 2.5x = 10 + 8 \\ \\ 3x = 18 \\ \\ x = \frac{18}{3} \\ \\ x = 6$

Answer 2

Finding the Boat's Speed

To find the boat's speed, we can use the formula: speed = distance / time

Let's denote: - x as the boat's speed in still water (in km/h) - y as the speed of the river's current (in km/h)

Given: - The boat travels the same distance in 3.5 hours on the lake and in 2 hours against the river's current as it does in 2.5 hours with the river's current. - The speed of the river's current is 4 km/h.

Calculating the Boat's Speed

1. Speed on the Lake: - The boat's speed on the lake is the sum of its speed in still water and the speed of the river's current, as it travels with the current. - So, the boat's speed on the lake is (x + 4) km/h.

2. Speed Against the River's Current: - The boat's speed against the river's current is the difference between its speed in still water and the speed of the river's current. - So, the boat's speed against the river's current is (x - 4) km/h.

3. Using the Given Information: - The boat travels the same distance in 3.5 hours on the lake and in 2 hours against the river's current as it does in 2.5 hours with the river's current. - This can be represented as the equation: distance = speed * time.

- For the lake: - Distance = (x + 4) * 3.5

- Against the river's current: - Distance = (x - 4) * 2

- With the river's current: - Distance = (x + 4) * 2.5

4. Solving the Equations: - By solving these equations, we can find the value of x, which represents the boat's speed in still water.

Let's calculate the boat's speed using the given information and the equations above.