Question

Лодка может проплыть некоторое расстояние за 4ч по течению реки и за 8ч против течения. Найди собственную скорость лодки и расстояние между пристанями, если скорость течения равна 2 км/ч.

Answer 1

$4(v+2)=8(v-2) \\\ 4v+8=8v-16 \\\ 24=4v \\\ v=6(km/h) \\\ s=4(6+2)=32(km)$
Ответ: 6км/ч, 32 км

Answer 2

Problem Analysis

We are given that a boat can travel a certain distance in 4 hours downstream (with the current) and the same distance in 8 hours upstream (against the current). We need to find the speed of the boat and the distance between the two docks, given that the speed of the current is 2 km/h.

Solution

Let's assume the speed of the boat is B km/h and the distance between the docks is D km.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. So, the boat's effective speed downstream is B + 2 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. So, the boat's effective speed upstream is B - 2 km/h.

We can use the formula speed = distance / time to calculate the distance traveled in each case.

Calculation

Let's calculate the distance traveled downstream and upstream using the given information.

Downstream: - Speed of the boat downstream = B + 2 km/h - Time taken downstream = 4 hours - Distance traveled downstream = (B + 2) * 4 km

Upstream: - Speed of the boat upstream = B - 2 km/h - Time taken upstream = 8 hours - Distance traveled upstream = (B - 2) * 8 km

Since the distance traveled downstream and upstream is the same, we can equate the two distances and solve for B.

((B + 2) * 4) = ((B - 2) * 8)

Simplifying the equation:

4B + 8 = 8B - 16

4B - 8B = -16 - 8

-4B = -24

B = 6

Now that we have the speed of the boat, we can calculate the distance between the docks.

Distance between the docks: - Speed of the boat = 6 km/h - Speed of the current = 2 km/h - Time taken downstream = 4 hours - Distance traveled downstream = (6 + 2) * 4 km = 32 km

Therefore, the distance between the docks is 32 km.

Answer

The speed of the boat is 6 km/h and the distance between the docks is 32 km.