Question

Катер за 3 ч по течению и 5 ч против течения проходит 92 км. За 5 ч по течению катер проходит на 10 км больше, чем за 6 ч против течения. Найдите собственную скорость катера и скорость течения. ПРОШУ!!! ПОМОГИТЕ!!!ОЧЕНЬ СРОЧНО НУЖНО!!! ОЧЕНЬ СРОЧНО!!! ПОЖАЛУЙСТА!!!

Answer 1

Пусть x - скорость катера 12/(x-3)+5/(x+3)=18/x 12(x+3)+5(x-3)-18(x^2-9) ____________________ =0 x(x-3)(x+3) 12x+36+5x-15-18x^2+162=0 -x^2+21+162=0 домножим на -1 x^2-21-162=0 a=1, b=-21, c=-162 D=b^2-4ac D=(-21)^2-4*1*(-162) x1=(21+корень 1089)/2 x2=(21-корень 1089)/2 x1=-6 x2=21 скорость всегда положительное число, значит ответ: 21

Answer 2

Problem Analysis

We are given the following information: - The boat travels downstream for 3 hours and covers a distance of 92 km. - The boat travels upstream for 5 hours and covers a distance of 92 km. - The boat travels downstream for 5 hours and covers a distance 10 km more than when it travels upstream for 6 hours.

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

Let's assume the speed of the boat is B km/h and the speed of the current is C km/h.

Solution

To solve this problem, we can use the formula: Distance = Speed × Time.

# Downstream Travel

When the boat travels downstream, it moves with the current, so the effective speed is the sum of the boat's speed and the current's speed.

The distance covered downstream is 92 km, and the time taken is 3 hours. Therefore, we have the equation:

92 = (B + C) × 3

# Upstream Travel

When the boat travels upstream, it moves against the current, so the effective speed is the difference between the boat's speed and the current's speed.

The distance covered upstream is 92 km, and the time taken is 5 hours. Therefore, we have the equation:

92 = (B - C) × 5

# Additional Information

When the boat travels downstream for 5 hours, it covers a distance that is 10 km more than when it travels upstream for 6 hours.

Let's calculate the distance covered downstream in 5 hours:

Distance downstream = (B + C) × 5

Let's calculate the distance covered upstream in 6 hours:

Distance upstream = (B - C) × 6

According to the given information, the distance downstream is 10 km more than the distance upstream:

Distance downstream = Distance upstream + 10

# Solving the Equations

We have three equations:

92 = (B + C) × 3 92 = (B - C) × 5 Distance downstream = Distance upstream + 10 We can solve these equations to find the values of B and C.

Let's solve the equations step by step.

From equation we can express C in terms of B:

C = (92 / 3) - B / 3 From equation we can express C in terms of B:

C = B / 5 - 92 / 5 Setting the expressions for C from equations and equal to each other, we can solve for B:

(92 / 3) - B / 3 = B / 5 - 92 / 5

Simplifying the equation:

10B / 15 = 184 / 15

B = 18.4

Now, substituting the value of B into equation we can solve for C:

C = (92 / 3) - (18.4 / 3)

C = 30.93

Therefore, the speed of the boat is 18.4 km/h and the speed of the current is 30.93 km/h.

Answer

The speed of the boat is 18.4 km/h and the speed of the current is 30.93 km/h.