Question

За 3 год за течією і 4 год проти течії теплохід проходить 380 км. За 1 год за течією і 30 хв проти течії теплохід проходить 85 км. Знайдіть власну швидкість теплохода і швидкість течії.

Answer 1

х - скорость теплохода

у - скорость течения

$\displaystyle\bf\\\left \{ {{3(x + y) + 4(x - y) = 380} \atop {x + y + 0.5(x - y) = 85 }} \right.\\ \displaystyle\bf\\\left \{ {{3x + 3y + 4x - 4y = 380} \atop {x + y + 0.5x - 0.5y = 85 }} \right. \\ \displaystyle\bf\\\left \{ {{7x - y = 380} \atop {1.5x + 0.5y = 85 \: \: | \times 2}} \right. \\ \displaystyle\bf\\ + \left \{ {{7x - y = 380} \atop {3x + y = 170 }} \right. \\ \\ 7x + 3x = 380 + 170 \\ 10x = 550 \\ x = 550 \div 10 \\ x = 55 \\ \\ 7 \times 55 - y = 380 \\ 385 - y = 380 \\ y = 385 - 380 \\ y = 5$

Ответ: скорость теплохода равна 55 км/год, а скорость течения реки - 5 км/год

Answer 2

Problem Analysis

We are given the following information: - The steamship travels 380 km downstream in 3 hours. - The steamship travels 85 km upstream in 1 hour and 30 minutes (or 1.5 hours).

We need to find the speed of the steamship and the speed of the current.

Solution

Let's assume the speed of the steamship is S km/h and the speed of the current is C km/h.

When the steamship is traveling downstream (with the current), its effective speed is the sum of its own speed and the speed of the current. Therefore, the equation for the downstream journey can be written as:

380 = (S + C) * 3 [[1]]

Similarly, when the steamship is traveling upstream (against the current), its effective speed is the difference between its own speed and the speed of the current. Therefore, the equation for the upstream journey can be written as:

85 = (S - C) * 1.5 [[2]]

We can solve these two equations simultaneously to find the values of S and C.

Solving the Equations

Let's solve the equations using the substitution method.

From equation [[2]], we can express S in terms of C:

S = (85 / 1.5) + C [[3]]

Substituting this value of S into equation [[1]], we get:

380 = ((85 / 1.5) + C + C) * 3

Simplifying the equation:

380 = (56.67 + 2C) * 3

380 = 170.01 + 6C

Rearranging the equation:

6C = 380 - 170.01

6C = 209.99

C = 34.9983

Substituting this value of C into equation [[3]], we can find the value of S:

S = (85 / 1.5) + 34.9983

S = 56.6667 + 34.9983

S = 91.665

Therefore, the speed of the steamship is approximately 91.665 km/h and the speed of the current is approximately 34.9983 km/h.

Please note that the values have been rounded for simplicity.

I hope this helps! Let me know if you have any further questions.