Question

Теплоход преодолевает 56 км за 2 часа по течению реки и 66 км за 3 часа против течения реки. Найдите: а) скорость течения реки? б) собственную скорость теплохода? (УРАВНЕНИЕМ) ​

Answer 1

Пусть х (км/ч) - собственная скорость теплохода, у (км/ч) - скорость течения реки, тогда (х + у) км/ч - скорость теплохода по течению реки, (х - у) км/ч - скорость теплохода против течения реки. Составим систему уравнений по условию задачи:

{(х + у) · 2 = 56

{(х - у) · 3 = 66

- - - - - - - - - - - -

{х + у = 56 : 2

{х - у = 66 : 3

- - - - - - - - - - - -

{х + у = 28

{х - у = 22

- - - - - - - - - - - -

Сложим оба уравнения системы

2х = 28 + 22

2х = 50

х = 50 : 2

х = 25

Подставим значение х в любое уравнение системы

25 + у = 28                  или             25 - у = 22

у = 28 - 25                                      у = 25 - 22

у = 3                                                у = 3

Ответ: а) 3 км/ч; б) 25 км/ч.

Answer 2

Task: Finding the speed of the river current and the speed of the boat

To find the speed of the river current and the speed of the boat, we can use the formula:

Speed = Distance / Time

Let's calculate the speed of the boat and the speed of the river current using the given information.

Given: - Distance traveled downstream (with the current) = 56 km - Time taken downstream = 2 hours - Distance traveled upstream (against the current) = 66 km - Time taken upstream = 3 hours

Calculating the speed of the river current (a)

To find the speed of the river current, we can use the formula:

Speed of the river current = (Speed downstream - Speed upstream) / 2

Let's calculate the speed of the river current:

1. Calculate the speed downstream: - Speed downstream = Distance downstream / Time downstream - Speed downstream = 56 km / 2 hours - Speed downstream = 28 km/h

2. Calculate the speed upstream: - Speed upstream = Distance upstream / Time upstream - Speed upstream = 66 km / 3 hours - Speed upstream = 22 km/h

3. Calculate the speed of the river current: - Speed of the river current = (Speed downstream - Speed upstream) / 2 - Speed of the river current = (28 km/h - 22 km/h) / 2 - Speed of the river current = 6 km/h / 2 - Speed of the river current = 3 km/h

Therefore, the speed of the river current is 3 km/h.

Calculating the speed of the boat (b)

To find the speed of the boat, we can use the formula:

Speed of the boat = Speed downstream - Speed of the river current

Let's calculate the speed of the boat:

1. Calculate the speed of the boat: - Speed of the boat = Speed downstream - Speed of the river current - Speed of the boat = 28 km/h - 3 km/h - Speed of the boat = 25 km/h

Therefore, the speed of the boat is 25 km/h.

In summary: - The speed of the river current is 3 km/h. - The speed of the boat is 25 km/h.

Please let me know if there is anything else I can help you with!