Question

Моторная лодка прошла от одной пристани до другой, расстояние между которыми по реке равно 16 км, сделала стоянку на 40 мин и вернулась обратно через 11/3 ч после начала поездки. Найдите скорость течения реки, если известно, что скорость моторной лодки в стоячей воде равна 12 км/ч.

Answer 1

пусть x-скорость течения реки.
тогда (х+12) - скорость лодки по течению,
(x-12) - скорость лордки против течения.
16/(x+12) - время, затраченное на путь по течению
16/(x-12)- время, затраченное на путь против течения,
стоянка была на 2/3 часа.
весь путь прошла за 3(2/3) часа.
отсюда получаем уравнение:
 16/(x+12)+16/(x-12)+2/3=3(2/3)
  16/(x+12)+16/(x-12)-3=0
16x-198+16x+198-3x^2+432=0
-3x^2+32+432=0   *(-1)
3x^2-32-432=0
D1=256-3*(-432)=1296
x=16(+-)36/2
x1=-10   не удовлетворяет условию, т.к отрицательное.
x2=2626 км/ч - скорость течения реки.
ответ:26 км/ч 

Answer 2

Calculation of River Current Speed

To find the speed of the river current, we can use the formula:

Speed of the boat in still water = Speed of the boat relative to the ground + Speed of the river current

Let's denote the speed of the boat in still water as B and the speed of the river current as C.

Given information: - Distance between the two docks: 16 km - Boat speed in still water: 12 km/h - Boat made a stop for 40 minutes - Boat returned back after 11/3 hours (which is 3 hours and 40 minutes) from the start of the trip

To solve this problem, we need to consider the time taken for the boat to travel from one dock to another and the time taken for the boat to return back.

Calculation of Time Taken for the Boat to Travel from One Dock to Another

Let's assume the time taken for the boat to travel from one dock to another is T hours.

The distance between the two docks is 16 km, and the boat's speed in still water is 12 km/h. Therefore, the time taken for the boat to travel from one dock to another can be calculated using the formula:

Time = Distance / Speed

Substituting the values, we have:

T = 16 km / 12 km/h

Simplifying, we find:

T = 4/3 hours

Calculation of Time Taken for the Boat to Return Back

The boat made a stop for 40 minutes, which is equal to 40/60 = 2/3 hours.

The boat returned back after 3 hours and 40 minutes, which is equal to 3 + 40/60 = 3 + 2/3 = 11/3 hours.

Therefore, the time taken for the boat to return back is 11/3 - 2/3 = 9/3 = 3 hours.

Calculation of Speed of the River Current

Now, let's calculate the speed of the river current.

When the boat is traveling from one dock to another, it is moving against the current. Therefore, the effective speed of the boat is the difference between the speed of the boat in still water and the speed of the river current.

Using the formula mentioned earlier, we have:

B = (B - C) + C

Simplifying, we find:

B = B - C + C

C = B - B

C = 0

This means that the speed of the river current is 0 km/h. Therefore, there is no current in the river.

Conclusion

Based on the given information, the speed of the river current is 0 km/h. This implies that there is no current in the river, and the boat's speed in still water is equal to its speed relative to the ground.

Please note that the calculation assumes a constant speed of the boat and a uniform river current.