Question

Из двух пунктов реки одновременно навстречу друг другу вышли две моторные лодки. Через 1,2 ч они встретились. Собственная скорость лодки, которая шла по течению реки, равна 18 км/ч, а лодки, которая шла против течения реки, 16 км/ч. До встречи одна лодка прошла на 9,6 км больше другой. Найдите скорость течения реки и расстояние, которое прошла каждая лодка до встречи.

Answer 1

Пусть Х ( км/час ) скорость течения реки ; 
( 18 + X ) * 1,2 - 9,6 = 1,2 * ( 16 - X )
21,6 + 1,2X - 9,6 = 19,2 - 1,2X 
1,2X + 1,2X = 19,2 - 12 
2,4X = 7,2 
X = 3 ( км/час ) скорость течения реки
---------------------------
Первая лодка прошла до встречи 
1,2 * ( 18 + 3 ) = 1,2 * 21 = 25,2 ( км )
Вторая лодка прошла до встречи
1,2 * ( 16 - 3 ) = 1,2 * 13 = 15,6 ( км ) 

Answer 2

Problem Analysis

We have two motorboats traveling towards each other on a river. One boat is traveling with the current at a speed of 18 km/h, while the other boat is traveling against the current at a speed of 16 km/h. The boats meet after 1.2 hours, and one boat has traveled 9.6 km more than the other boat. We need to find the speed of the river's current and the distance each boat traveled before they met.

Solution

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

To find the distance each boat traveled, we can use the formula: distance = speed × time.

Let's calculate the distance traveled by the boat going with the current: - Speed of the boat = 18 km/h - Time = 1.2 hours - Distance = 18 km/h × 1.2 hours = 21.6 km

Now, let's calculate the distance traveled by the boat going against the current: - Speed of the boat = 16 km/h - Time = 1.2 hours - Distance = 16 km/h × 1.2 hours = 19.2 km

According to the problem, one boat traveled 9.6 km more than the other boat. Let's assume that the boat going with the current traveled this additional distance. Therefore, the distance traveled by the boat going with the current is 21.6 km + 9.6 km = 31.2 km, and the distance traveled by the boat going against the current is 19.2 km.

To find the speed of the river's current, we can use the formula: speed of the river's current = (speed of the boat going with the current - speed of the boat going against the current) / 2.

Let's substitute the values into the formula: - Speed of the boat going with the current = 18 km/h - Speed of the boat going against the current = 16 km/h - Speed of the river's current = (18 km/h - 16 km/h) / 2 = 1 km/h

Therefore, the speed of the river's current is 1 km/h.

To summarize: - The speed of the river's current is 1 km/h. - The boat going with the current traveled 31.2 km before they met. - The boat going against the current traveled 19.2 km before they met.

Please let me know if anything is unclear or if you need further assistance!