Question

Рыболов проплыл на лодке от пристани некоторое расстояние вверх по течению реки, затем бросил якорь, 2 часа ловил рыбу и вернулся обратно через 6 часов от начала путешествия. На какое расстояние от пристани он отплыл, если скорость течению реки равна 1км/ч, а собственная скорость лодки 5 км/ч?

Answer 1

х км - от пристани отплыл рыболов,

x/(5-1)+x/(5+1)=6-2,

x/4+x/6=4,

3x+2x=48,

5x=48,

x=9,6.

Answer 2

Расстояние берем за х, скорость по течению 6 км/ч, против течения 4 км/ч. Время по течению равно х/6, против течения х/4, плюс он стоял 2 часа. Всё время 6 часов.

х/6+х/4+2=6 НОЗ:12

2х+3х+24=72

5х=48

х=9,6

Answer 3

Problem Analysis

A fisherman sets off on a boat from a dock and travels a certain distance upstream against the current of a river. He then drops anchor, spends 2 hours fishing, and returns back to the dock in a total of 6 hours. We need to determine the distance the fisherman traveled from the dock if the speed of the river's current is 1 km/h and the speed of the boat is 5 km/h.

Solution

Let's assume the distance the fisherman traveled from the dock is d km.

When the fisherman is traveling upstream against the current, the effective speed of the boat is the difference between the boat's speed and the current's speed. So, the effective speed is 5 km/h - 1 km/h = 4 km/h.

The time taken to travel upstream is given by the equation: time taken upstream = distance / effective speed

Using this equation, we can calculate the time taken upstream as d / 4 hours.

After dropping anchor, the fisherman spends 2 hours fishing.

The time taken to return downstream is given by the equation: time taken downstream = distance / (boat speed + current speed)

Using this equation, we can calculate the time taken downstream as d / (5 + 1) = d / 6 hours.

The total time taken for the entire trip is given as 6 hours.

So, the equation becomes: time taken upstream + time spent fishing + time taken downstream = total time

Substituting the values, we get: d / 4 + 2 + d / 6 = 6

To solve this equation, we can multiply through by the common denominator of 12 to eliminate the fractions: 3d + 24 + 2d = 72

Combining like terms, we get: 5d + 24 = 72

Simplifying further, we have: 5d = 48

Dividing both sides by 5, we find: d = 9.6

Therefore, the fisherman traveled a distance of 9.6 km from the dock.

Answer

The fisherman traveled a distance of 9.6 km from the dock.

Explanation

The fisherman traveled upstream for a certain distance, spent 2 hours fishing, and then returned downstream to the dock. The effective speed of the boat upstream is 4 km/h, and the time taken upstream is d / 4 hours. The time taken downstream is d / 6 hours. The total time for the trip is 6 hours. By solving the equation d / 4 + 2 + d / 6 = 6, we find that the fisherman traveled a distance of 9.6 km from the dock.