Question

Прогулочный теплоход по течению реки проплывает 12км за такое же время, что и 10км против течения.Найдите скорость течения реки, если собственная скорость теплохода 22км/ч

Answer 1

Обозначим за х скрость течения реки,
22+х скорость теплохода по течению
22-х скорость теплохода против течения
12/(22+х) время, за которое теплоход проплывет 12 км по течению
10/(22-х) время, за которое теплоход проплывет 10 км против течения
По условию задачи эти два времени равны, приравниваем
12,/(22+х) =10/(22-х)
переносим вправо и рприводим к общему знаменателю
получаем числитель 12(22-х) -10(22+х) =0
12*22-12х-10*22-10х=0
Проверка
Скорость по течению 24, пройдет 12 км за 5мин
Скорость против течения 20 пройдет 10км за 5мин
-22х=-44
х=2

Answer 2

Problem Analysis

We are given that a pleasure boat travels 12 km downstream in the same amount of time it takes to travel 10 km upstream. We need to find the speed of the river's current, given that the boat's speed is 22 km/h.

Solution

Let's assume the speed of the river's current is x km/h.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's effective speed is 22 + x km/h.

Similarly, when the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's effective speed is 22 - x km/h.

We are given that the boat takes the same amount of time to travel 12 km downstream as it does to travel 10 km upstream. This can be expressed as the following equation:

Time taken downstream = Time taken upstream

To find the time taken, we can use the formula time = distance / speed.

For the downstream journey: Time taken downstream = 12 / (22 + x)

For the upstream journey: Time taken upstream = 10 / (22 - x)

Since the times are equal, we can set up the following equation:

12 / (22 + x) = 10 / (22 - x)

To solve this equation, we can cross-multiply and simplify:

12(22 - x) = 10(22 + x)

Simplifying further:

264 - 12x = 220 + 10x

Combining like terms:

22x = 44

Dividing both sides by 22:

x = 2

Therefore, the speed of the river's current is 2 km/h.

Answer

The speed of the river's current is 2 km/h.