Question

Моторная лодка прошла по течению реки 28 км и против течения 25 км. На весь путь она потратила столько времени, сколько бы потратила для прохождения 54 км в стоячей воде .Найдите скорость лодки в стоячей воде если скорость течения 2 км/ч

Answer 1

Пусть собственная скорость лодки х км\час (скорость лодки в стоячей воде), тогда скорость лодки по течению реки равна х+2 км\час, против течения реки х-2 км\час. по условию задачи составляем уравение:

$></p><p>значит скорость лодки в сточей воде 12 км\час.</p><p>ответ:<strong> 12 км\час</strong></p></div> <div class=$ 0 0

Answer 2

28/(x+2)+25/(х-2)=54/х

х^2+6х-216=0

х1=-18,х2=12

ответ:12

Answer 3

Problem Analysis

We are given that a motorboat traveled 28 km downstream and 25 km upstream on a river. The boat's speed relative to the water is unknown, but the speed of the river's current is given as 2 km/h. We need to find the speed of the boat in still water.

Downstream Speed

When the boat is traveling downstream, its speed is increased by the speed of the current. Let's denote the speed of the boat in still water as x km/h. Therefore, the boat's speed downstream is (x + 2) km/h.

Upstream Speed

When the boat is traveling upstream, its speed is decreased by the speed of the current. Therefore, the boat's speed upstream is (x - 2) km/h.

Time Calculation

We are also given that the boat took the same amount of time to travel the total distance of 28 km downstream and 25 km upstream as it would take to travel 54 km in still water. Let's denote the time taken for both scenarios as t.

The time taken to travel a certain distance is equal to the distance divided by the speed. Therefore, we can set up the following equation for the downstream and upstream scenarios:

Downstream: 28 / (x + 2) = t Upstream: 25 / (x - 2) = t Still water: 54 / x = t

Solving the Equations

We can solve these equations to find the value of x, which represents the speed of the boat in still water.

Let's start by solving the equation for t in terms of x from the downstream and upstream scenarios:

28 / (x + 2) = 25 / (x - 2)

To solve this equation, we can cross-multiply:

28(x - 2) = 25(x + 2) 28x - 56 = 25x + 50 3x = 106 x = 35.33

Therefore, the speed of the boat in still water is approximately 35.33 km/h.

Answer

The speed of the boat in still water is approximately 35.33 km/h.