Question

Катер шел по течению реки 180 км, а затем вернулся обратно, причем на обратный путь было затрачено на 8 часов больше. Скорость течения реки равна 4 км/ч. Найди собственную скорость катера (в км/ч)

Answer 1

Ответ:14 км/час

Пошаговое объяснение:

Пусть собственная  скорость катера x км/ч. Тогда скорость катера по течению x+4 , а против течения равна х-4 . Прошел расстояние 180 км, причем на обратный путь было затрачено на 8 часов больше.

V=S/t

$\frac{180}{x-4} -\frac{180}{x+4} =8\\180*(x+4)-180*(x-4)=8*(x^{2} -4^{2}) \\\\180x+720-180x+720=8x^{2} -128\\1440+128=8 x^{2} \\8x^{2} =1568 (:8)\\x^{2} =196\\x_{1} =-14\\x_{2} =+14$

Отрицательная скорость быть не может

Answer 2

Problem Analysis

We are given that a boat traveled downstream along a river for a distance of 180 km and then returned back. The total time taken for the return trip was 8 hours longer than the downstream trip. The speed of the river current is given as 4 km/h. We need to find the speed of the boat.

Downstream Trip

Let's assume the speed of the boat in still water is x km/h. During the downstream trip, the boat's speed is increased by the speed of the river current, so the effective speed is (x + 4) km/h.

The time taken for the downstream trip can be calculated using the formula: Time = Distance / Speed

The distance traveled during the downstream trip is 180 km, and the speed is (x + 4) km/h. Therefore, the time taken for the downstream trip is: Time_downstream = 180 / (x + 4)

Upstream Trip

During the upstream trip, the boat's speed is decreased by the speed of the river current, so the effective speed is (x - 4) km/h.

The time taken for the upstream trip can be calculated using the same formula: Time = Distance / Speed

The distance traveled during the upstream trip is also 180 km, and the speed is (x - 4) km/h. Therefore, the time taken for the upstream trip is: Time_upstream = 180 / (x - 4)

Relationship between Time Downstream and Time Upstream

We are given that the time taken for the return trip (upstream) is 8 hours longer than the downstream trip. Mathematically, we can express this as: Time_upstream = Time_downstream + 8

Substituting the expressions for Time_upstream and Time_downstream, we get: 180 / (x - 4) = 180 / (x + 4) + 8

Solving the Equation

To solve the equation, we can start by multiplying both sides by (x - 4)(x + 4) to eliminate the denominators: 180(x - 4) = 180(x + 4) + 8(x - 4)(x + 4)

Simplifying the equation gives: 180x - 720 = 180x + 720 + 8(x^2 - 16)

Simplifying further: 180x - 720 = 180x + 720 + 8x^2 - 128

Combining like terms: 0 = 8x^2 - 128

Dividing both sides by 8: x^2 - 16 = 0

Factoring the quadratic equation: (x - 4)(x + 4) = 0

Setting each factor equal to zero gives two possible solutions: x - 4 = 0 or x + 4 = 0

Solving for x gives: x = 4 or x = -4

Since the speed of the boat cannot be negative, we can conclude that the speed of the boat in still water is 4 km/h.

Answer

The speed of the boat in still water is 4 km/h.