Question

За 9 часов по течению реки катер проходит то же растояние что за 11 часов против течения. Найдите собственную скорость катера если скорость течения реки 2 км/ч

Answer 1

Скорость катера х, тогда по течению х+2, против течения х-2.
9*(х+2)=11*(х-2)
решаем уровнение и получаем х=10 км/ч

Answer 2

Problem Analysis

We are given that a boat takes 9 hours to travel a certain distance downstream (with the current) and 11 hours to travel the same distance upstream (against the current). We need to find the speed of the boat in still water.

Let's assume the speed of the boat in still water is x km/h, and the speed of the river current is 2 km/h.

Downstream Speed

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river current. Therefore, the boat's speed downstream is (x + 2) km/h.

Upstream Speed

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current. Therefore, the boat's speed upstream is (x - 2) km/h.

Distance Calculation

Since the boat covers the same distance in both directions, we can use the formula:

Distance = Speed × Time

Let's calculate the distance traveled downstream and upstream.

Distance Downstream

The boat takes 9 hours to travel downstream, so the distance traveled downstream is:

Distance Downstream = (x + 2) km/h × 9 hours

Distance Upstream

The boat takes 11 hours to travel upstream, so the distance traveled upstream is:

Distance Upstream = (x - 2) km/h × 11 hours

Since the distances traveled downstream and upstream are the same, we can set up the following equation:

(x + 2) km/h × 9 hours = (x - 2) km/h × 11 hours

Now, let's solve this equation to find the value of x, which represents the boat's speed in still water.

Solving the Equation

To solve the equation, we can start by expanding it:

9(x + 2) = 11(x - 2)

Simplifying further:

9x + 18 = 11x - 22

Bringing the x terms to one side and the constant terms to the other side:

9x - 11x = -22 - 18

Simplifying:

-2x = -40

Dividing both sides by -2:

x = 20

Therefore, the speed of the boat in still water is 20 km/h.

Answer

The speed of the boat in still water is 20 km/h.