Question

Катер проходит расстояние между двумя пристанями по течению реки за 2 ч, а плот – за 8 ч. Какое время затратит катер на обратный путь? Дайте ответ в часах.

Answer 1

V(п)=S/8 (Скорость плота, она же скорость течения)
V(к) - скорость катера
V(т) - скорость течения
(V(к)+V(т))*2=S
(V(к)+S/8)*2=S
V(к)=S/2-S/8=(3/8)S (собственная скорость катера)
(V(к)-S/8)*t=S
((3/8)S-S/8)*t=S
1/4S*t=S
t=S:((1/4)S)=4
Ответ: на обратную дорогу катер затратит 4 часа.

Answer 2

Problem Analysis

We are given that a boat travels a distance between two piers downstream in 2 hours, while a raft takes 8 hours to cover the same distance downstream. We need to determine how long it will take for the boat to travel the same distance upstream.

Solution

Let's assume that the distance between the piers is d.

We can use the formula: speed = distance / time.

The speed of the boat downstream is d / 2 (since it covers the distance in 2 hours), and the speed of the raft downstream is d / 8 (since it covers the distance in 8 hours).

To find the speed of the boat upstream, we need to consider the effect of the river's current. Let's assume the speed of the river's current is c.

The speed of the boat relative to the water upstream is (d / 2) - c (since the current opposes the boat's motion), and the speed of the raft relative to the water upstream is (d / 8) - c.

Since the boat and the raft cover the same distance, we can equate their relative speeds:

(d / 2) - c = (d / 8) - c

Simplifying the equation, we get:

(d / 2) = (d / 8)

Solving for d, we find that d = 8.

Therefore, the distance between the piers is 8 units.

Now, we need to find the time it takes for the boat to travel the distance upstream. We can use the formula time = distance / speed.

The speed of the boat upstream is (d / 2) + c (since the current aids the boat's motion).

Substituting the values, we get:

time = 8 / ((8 / 2) + c)

Simplifying the equation, we get:

time = 8 / (4 + c)

Therefore, the boat will take 8 / (4 + c) hours to travel the distance upstream.

Answer

The boat will take 8 / (4 + c) hours to travel the distance upstream, where c is the speed of the river's current.