Question

Рыболов в 5 часов утра на моторной лодке отправился от пристани против течения реки, через некоторое время бросил якорь, 2 часа ловил рыбу и вернулся обратно в 10 часов утра того же дня. На какое расстояние от пристани он отдалился, если скорость реки равна 2 км/ч, а собственная скорость лодки 6 км/ч? Дать развернутый ответ.

Answer 1

6 + 2 = 8 (км/ч) - скорость лодки по течению.
6 - 2 = 4 (км/ч) - скорость лодки против течения.
10 - 5 = 5 (ч) - общее время в пути вместе с ловлей рыбы.
5 - 2 = 3 (ч) - время в пути.
Пусть х км - расстояние от пристани до места ловли рыбы.
х : 8 + х : 4 = 3
4х + 8х = 3 * 4 * 8
12х = 96
х = 96 : 12
х = 8 (км) - расстояние от пристани до места ловли рыбы.
Ответ: 8 км.

Answer 2

Problem Analysis

A fisherman sets off from the dock at 5:00 AM in a motorboat against the current of a river. After some time, he drops anchor, spends 2 hours fishing, and then returns to the dock at 10:00 AM on the same day. We need to determine how far he traveled from the dock. We are given that the speed of the river is 2 km/h and the speed of the boat is 6 km/h.

Solution

To solve this problem, we need to consider the relative speeds of the boat and the river. When the boat is moving against the current, the effective speed is the difference between the boat's speed and the river's speed. When the boat is moving with the current, the effective speed is the sum of the boat's speed and the river's speed.

Let's break down the problem into different stages:

1. The fisherman sets off from the dock at 5:00 AM. Since he is moving against the current, the effective speed is the boat's speed minus the river's speed. Therefore, the fisherman's effective speed is 6 km/h - 2 km/h = 4 km/h.

2. After some time, the fisherman drops anchor. During this time, the fisherman is stationary, so the distance traveled is 0 km.

3. The fisherman spends 2 hours fishing. Since he is stationary during this time, the distance traveled is still 0 km.

4. The fisherman starts his return journey at 10:00 AM. Now, he is moving with the current, so the effective speed is the boat's speed plus the river's speed. Therefore, the fisherman's effective speed is 6 km/h + 2 km/h = 8 km/h.

5. The fisherman returns to the dock at 10:00 AM. The total time for the return journey is 10:00 AM - 5:00 AM = 5 hours.

Now, let's calculate the distance traveled by the fisherman during the return journey:

Distance = Speed × Time

Distance = 8 km/h × 5 h = 40 km

Therefore, the fisherman traveled a distance of 40 km from the dock.

Answer

The fisherman traveled a distance of 40 km from the dock.