Question

Т пристани А до пристани В лодка плыла против течения реки 5 ч 24 мин. На обратный путь она затратила 3,6 ч . Какое расстояние преодолела лодка за все время движения, если скорость течения реки 2 км/ч? Ответ запишите в километрах целым числом или десятичной дробью без наименования.

Answer 1

Дано:
t₁= 5 ч. 24 мин. = 5 ²⁴/₆₀ ч. = 5,4 ч.  -  время на путь против течению реки
t₂ = 3,6 ч.    - время на путь по течению реки
Vт  = 2 км/ч -  скорость течения
S₁=S₂  - расстояние АВ 
Найти:  S₁+ S₂ =? 
Решение.
Собственная скорость лодки Vc = x  км/ч
Путь против течения  S₁ = t₁(Vc - Vт)   = 5.4 * (x - 2)
Путь по течению  S₂ = t₂(Vc+Vт) = 3,6 *(х + 2)
Зная, что S₁ = S₂ , составим уравнение:
5,4(х-2) = 3,6(х+2) 
5,4х  - 5,4*2  = 3,6х + 3,6*2
5,4х  - 10,8  = 3,6х  + 7,2
5,4х - 3,6х = 7,2 + 10,8
1,8х = 18
х = 18 : 1,8
х = 10  (км/ч)    ⇒ Vc = 10 (км/ч)  собственная скорость лодки
S₁+S₂ = 5,4 *(10-2) +3,6 *(10+2)  = 5,4 *8 + 3,6 *12 =43.2 +43.2 = 86,4 (км) 
расстояние, которое преодолела лодка за всё время движения.

Ответ: 86,4  .

Answer 2

Calculation of Distance Traveled by the Boat

To calculate the distance traveled by the boat, we need to consider the time taken for both the upstream and downstream journeys.

Given: - Time taken for the boat to travel from port A to port B against the river current: 5 hours 24 minutes - Time taken for the boat to travel from port B back to port A with the river current: 3.6 hours - Speed of the river current: 2 km/h

To find the distance traveled by the boat, we can use the formula:

Distance = Speed x Time

Let's calculate the distance for each leg of the journey and then find the total distance traveled.

Distance Traveled Against the River Current

The boat traveled from port A to port B against the river current. The time taken for this journey is 5 hours 24 minutes.

Converting the time to hours: 5 hours 24 minutes = 5 + (24/60) hours = 5.4 hours

To find the distance traveled against the river current, we can use the formula:

Distance = Speed x Time

Substituting the values: Distance = 2 km/h x 5.4 hours

Calculating the distance: Distance = 10.8 km

Distance Traveled With the River Current

The boat traveled from port B back to port A with the river current. The time taken for this journey is 3.6 hours.

To find the distance traveled with the river current, we can again use the formula:

Distance = Speed x Time

Substituting the values: Distance = 2 km/h x 3.6 hours

Calculating the distance: Distance = 7.2 km

Total Distance Traveled

To find the total distance traveled by the boat, we can add the distances traveled against and with the river current:

Total Distance = Distance Against Current + Distance With Current

Substituting the values: Total Distance = 10.8 km + 7.2 km

Calculating the total distance: Total Distance = 18 km

Therefore, the boat traveled a total distance of 18 kilometers during the entire journey.