Question

Лодка в 8:00 вышла из пункта а в пункт б , расположенный в 24км от а. Пробыв в пункте 3 ч лодка отправилась обратно и вернулась в пункт а в 21:00. Определите скорость лодки , если известно, что скорость течения реки 1км/ч

Answer 1

Скорость лодки:  v км/ч
Допустим, что первую часть пути лодка шла по течению.
Тогда из пункта А в пункт Б лодка шла:
                           t₁ = S/(v+v₀) (ч), где v₀ = 1 км/ч - скорость течения реки.
Обратно лодка шла:
                           t₂ = S/(v-v₀) (ч)
Так как t = t₁+t₂ = 21 - 8 - 3 = 10 (ч), то:
                           t₁+t₂ = S/(v+v₀) + S/(v-v₀)
                           10 = (24(v-v₀) + 24(v+v₀)):(v²-v₀²)
                           24v - 24v₀ + 24v + 24v₀ = 10(v²-v₀²)
                           5v² - 24v - 5 = 0       D = b²-4ac = 576+100 = 676 = 26²

                             v₁ = (-b+√D)/2a = (24+26):10 = 5 (км/ч)
                             v₂ = (-b -√D)/2a = - 0,2 - не удовлетворяет условию.

Ответ: скорость лодки 5 км/ч.  

Answer 2

Calculation of Boat Speed

To determine the speed of the boat, we can use the formula:

Speed = Distance / Time

Given that the boat traveled from point A to point B, a distance of 24 km, and then returned to point A, we can calculate the total distance traveled by the boat as:

Total Distance = 2 * Distance AB

where Distance AB is the distance from point A to point B.

Since the boat traveled from point A to point B in the morning and returned to point A in the evening, we can calculate the total time taken as:

Total Time = Time AB + Time BA

where Time AB is the time taken to travel from point A to point B, and Time BA is the time taken to travel from point B back to point A.

Given that the boat left point A at 8:00 and returned to point A at 21:00, we can calculate the total time taken as:

Total Time = Time AB + Time BA = (21:00 - 8:00) = 13 hours

Now, we know that the speed of the river current is 1 km/h. This means that the boat's speed relative to the ground is the difference between its actual speed and the speed of the current.

Let's assume the boat's speed is represented by V km/h.

To calculate the boat's speed, we can use the following equation:

Total Distance = (V + 1) * Total Time

Substituting the known values, we have:

2 * Distance AB = (V + 1) * 13

Simplifying the equation, we get:

24 km = 13V + 13

13V = 24 - 13

13V = 11

V = 11 / 13

V ≈ 0.846 km/h

Therefore, the speed