Question

Катер с собственной скоростью 20км/ч проплыл 4ч по течению реки и 6ч-против течения.Весь путь катера составил 196км.Найти скорость течения реки.

Answer 1

Решение:
Пусть х - скорость течения реки,
тогда( 20+х) - скорость катера по течению,
а (20-х) - скорость катера против течения
Составим и решим уравнение:

4×(20+х)+6×(20-х)=196
80+4х+120-6х=196
200-2х=196
2х=200-196
2х=4
х=2

2 км/ч - скорость течение реки

Ответ: 2 км/ч

Answer 2

Problem Analysis

To find the speed of the river current, we can set up a system of equations based on the given information. Let's assume the speed of the river current is represented by x km/h.

According to the problem, the boat traveled downstream (with the current) for 4 hours and upstream (against the current) for 6 hours. The total distance traveled by the boat is 196 km.

Downstream Speed

When the boat is traveling downstream, the speed of the boat relative to the river current is the sum of the boat's own speed and the speed of the current. Therefore, the boat's speed downstream is 20 + x km/h.

Since the boat traveled downstream for 4 hours, the distance covered is the product of the speed and time: (20 + x) * 4 km.

Upstream Speed

When the boat is traveling upstream, the speed of the boat relative to the river current is the difference between the boat's own speed and the speed of the current. Therefore, the boat's speed upstream is 20 - x km/h.

Since the boat traveled upstream for 6 hours, the distance covered is the product of the speed and time: (20 - x) * 6 km.

Total Distance

The total distance traveled by the boat is given as 196 km. Therefore, we can set up the equation:

(20 + x) * 4 + (20 - x) * 6 = 196

Now, we can solve this equation to find the value of x, which represents the speed of the river current.