Question

Лодка проплыла от одной станции до другой против течения реки за 4 ч. Обратный путь занял у неё 3 ч. Скорость течения реки 1 км/ч.Найдите собственную скорость лодки.

Answer 1

пусть х км в час - собственная скорость лодки

тогда скорость по течению х+1 и за 3 часа пройдено 3(x+1) км.

против течения скорость х-1 и за 4 часа пройдено 4(х-1) км.

приравниваем, получаем ур-е

 

3(х+1) = 4(х-1)

х = 7 (км/ч)

 

Answer 2

пусть х км в час - собственная скорость лодки

тогда скорость по течению х+1 и за 3 часа пройдено 3(x+1) км.

против течения скорость х-1 и за 4 часа пройдено 4(х-1) км.

приравниваем, получаем ур-е

 

3(х+1) = 4(х-1)

х = 7 (км/ч)

 

V собственная ? Х км/ч

V течения реки 1 км/ч

V по течению реки = V собственная + Vреки

V против течения реки = Vсобственная - V реки

Пусть х км/ч – собственная скорость, (х+1)км/ч скорость по течению реки,(х-1) км/ч скорость против течения реки.за 3 часа пройдено 3(x+1) км,а за 4 часа пройдено 4(х-1) км.

Известно, что расстояние по течению и против течения одинаковое.

Составляем уравнение.

    3(х+1) = 4(х-1)

3х+3 = 4х-4

3х-4х = -4-3

-х = -7

х =7

х = 7 (собственная скорость)

 

Ответ: Собственная скорость 7 км/ч,

Answer 3

Calculation of the Boat's Speed

To find the boat's speed, we need to consider the time it took for the boat to travel from one station to another both against the current and with the current.

Let's denote the boat's speed as x km/h and the speed of the river's current as 1 km/h.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. Therefore, the boat's effective speed is (x - 1) km/h.

According to the given information, the boat took 4 hours to travel from one station to another against the current. Using the formula distance = speed × time, we can calculate the distance traveled:

Distance against current = (x - 1) × 4 km. Similarly, when the boat is traveling with the current, its effective speed is increased by the speed of the current. Therefore, the boat's effective speed is (x + 1) km/h.

According to the given information, the boat took 3 hours to travel from one station to another with the current. Using the formula distance = speed × time, we can calculate the distance traveled:

Distance with current = (x + 1) × 3 km. Since the distance traveled is the same in both cases, we can equate the two distances:

(x - 1) × 4 = (x + 1) × 3

Now, let's solve this equation to find the value of x:

4x - 4 = 3x + 3

x = 7

Therefore, the boat's speed is 7 km/h.

Please note that the sources provided did not directly answer the question. The calculation was done based on the given information and mathematical principles.