Question

моторная лодка прошла вниз по течению реки 14 км.,а затем 9 км против течения,затратив на весь путь 5 часов.Найдите скорость течения реки,если скорость моторной лодки в стоячей воде равна 5 км/ч.

Answer 1

пусть х скорость течеения

14/(x+5)+9/(5-x)=5

70-14x+9x+45=5(25-x^2)

115-5x=25*5-5x^2

5x^2-5x+115-125=0

5x^2-5x-10=0

x^2-x-2=0

x1=-1

x2=2

значение скорости не может быть меньще нуля.

ответ x=2 км в час

Answer 2

x - скорость течения реки

5+х - скорость лодки по течению

5-х - скорость лодки против течения

14/(5+х)+9/(5-х)=5

14(5-х)+ 9(5+х)=5(25-х²)

5х²-125+70-14х+45+9х=0

5x²-5x-10=0

x²-x-2=0

По теореме Виета

x1=2

x2=-1 (не учитываем)

Скорость течения реки - 2 км/час

Answer 3

Problem Analysis

To find the speed of the river current, we can use the formula: Speed of boat in still water = (Speed downstream + Speed upstream) / 2 and Speed of current = (Speed downstream - Speed upstream) / 2

Given: - Distance downstream = 14 km - Distance upstream = 9 km - Total time = 5 hours - Speed of boat in still water = 5 km/h

Calculation

Using the given data, we can calculate the speed of the river current.

The speed downstream can be calculated using the formula: Speed downstream = Distance downstream / Time downstream

The speed upstream can be calculated using the formula: Speed upstream = Distance upstream / Time upstream

Then, we can use the formulas mentioned in the problem analysis to find the speed of the river current.

Solution

Let's calculate the speed of the river current using the provided information.

First, we calculate the speed downstream: Speed downstream = Distance downstream / Time downstream Speed downstream = 14 km / (5 hours - Time upstream)

Then, we calculate the speed upstream: Speed upstream = Distance upstream / Time upstream Speed upstream = 9 km / Time upstream

Now, we can use the formulas to find the speed of the river current: Speed of boat in still water = (Speed downstream + Speed upstream) / 2 Speed of current = (Speed downstream - Speed upstream) / 2

Let's proceed with the calculations.