Question

Теплоход проходит по течению реки до пункта назначения 780 км и после стоянки возвращается в пункт отправления. Найдите скорость течения, если скорость теплохода в неподвижной воде равна 28 км/ ч, стоянка длится 4 ч, а в пункт отправления теплоход возвращается через 60 ч после отплытия из него.

Answer 1

Х - скорость течения
время теплохода в движении =60-4=56 ч.
скорость теплохода туда = 28+ х 
скорость обратно = 28 - х
время туда и обратно = 780/(28+х) + 780/ (28-х) = 56
приведем к общему знаменателю
(780(28-х)+780(28+х))/((28+х)*(28-х))=56
(780*56)/(784-х^2)=56
784-х^2=780
x^2=4
x=2 (так как скорость - величина положительная, х не равно "-2"

Ответ: 2 км\ч

Answer 2

Problem Analysis

We are given the following information: - The distance from the starting point to the destination is 780 km. - The speed of the boat in still water is 28 km/h. - The boat stays at the destination for 4 hours. - The boat returns to the starting point after 60 hours of departure.

We need to find the speed of the river current.

Solution

Let's assume the speed of the river current is x km/h.

When the boat is going from the starting point to the destination, it is moving against the current. So the effective speed of the boat is the difference between the speed of the boat in still water and the speed of the river current: 28 - x km/h.

Similarly, when the boat is returning from the destination to the starting point, it is moving with the current. So the effective speed of the boat is the sum of the speed of the boat in still water and the speed of the river current: 28 + x km/h.

We can use the formula speed = distance / time to calculate the time taken for each leg of the journey.

Let's calculate the time taken for each leg of the journey:

- Time taken from the starting point to the destination: 780 / (28 - x) hours. - Time taken from the destination to the starting point: 780 / (28 + x) hours.

According to the given information, the boat stays at the destination for 4 hours and returns to the starting point after 60 hours of departure. Therefore, the total time for the round trip is the sum of the time taken for each leg of the journey, the time spent at the destination, and the time taken for the return journey: 780 / (28 - x) + 4 + 780 / (28 + x) + 60 hours.

Since the total distance covered in the round trip is 1560 km (780 km from the starting point to the destination and 780 km from the destination to the starting point), we can set up the equation:

1560 = 780 / (28 - x) + 4 + 780 / (28 + x) + 60

Now we can solve this equation to find the value of x, which represents the speed of the river current.

Calculation

Let's solve the equation to find the value of x:

1560 = 780 / (28 - x) + 4 + 780 / (28 + x) + 60

Simplifying the equation:

1560 = 780 / (28 - x) + 780 / (28 + x) + 64

Multiplying through by the common denominator:

1560(28 - x)(28 + x) = 780(28 + x) + 780(28 - x) + 64(28 - x)(28 + x)

Expanding and simplifying:

1560(784 - x^2) = 1560(56) + 64(784 - x^2)

Simplifying further:

1560(784 - x^2) = 87360 + 4992 - 64x^2

Combining like terms:

12221440 - 1560x^2 = 92352 - 64x^2

Rearranging the equation:

1496x^2 = 12129088

Dividing both sides by 1496:

x^2 = 8112

Taking the square root of both sides:

x = sqrt(8112) ≈ 90.06

Therefore, the speed of the river current is approximately 90.06 km/h.

Answer

The speed of the river current is approximately 90.06 km/h.