Question

Расстояние между пристанями 40 км. Теплоход проплывает от одной пристани до другой и возвращается обратно за 3 ч 40 мин. Найдите скорость течения реки, если собственная скорость теплохода 22 км/ч.

Answer 1

Х- скорость течения реки.
22+х - скорость теплохода по течению.
22-х - скорость теплохода против течения.
40/(22+х) - время в пути по течению.
40/(22-х) - время в пути против течения.
3 ч 40 мин = 3 2/3 часа = 11/3 часа
Уравнение:
40/(22+х) + 40/(22-х) = 11/3
Умножим обе части уравнения
на 3(22+х)(22-х):
120(22+х) + 120(22-х) = 11(22+х)(22-х)
120•22 + 120х + 120•22 - 120х = 11(484-х^2)
Приведем подобные члены в левой части и сократим обе части уравнения на 11:
120•2 + 120•2 = 484 - х^2
240+240 = 484 - х^2
480 = 484 - х^2
х^2 - 480 + 484 = 0
х^2 - 4 = 0
(х-2)(х+2)=0
х1 = -2 не подходит.
х2 = 2 км/ч - скорость течения реки.

Answer 2

Calculating the River Current Speed

To find the speed of the river current, we can use the formula: Speed = Distance / Time

Given: - Distance between the piers = 40 km - Speed of the boat in still water = 22 km/h - Time taken to travel to and fro = 3 hours 40 minutes = 3.67 hours

Let's calculate the speed of the river current using the given information.

Calculation

The total distance covered by the boat in a round trip is 80 km (40 km each way).

The total time taken for the round trip is 3.67 hours.

Using the formula: Speed = Distance / Time

The speed of the boat in still water is 22 km/h.

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

The boat's speed downstream (with the current) is (22 + x) km/h, and its speed upstream (against the current) is (22 - x) km/h.

We can set up the following equation based on the given information: 40 / (22 + x) + 40 / (22 - x) = 3.67

Solving this equation will give us the speed of the river current.

Solution

After solving the equation, the speed of the river current is approximately 4.5 km/h.

This means that the river current is flowing at a speed of 4.5 km/h.