Question

Расстояние между двумя пристанями равно 90 км. Это расстояние лодка проплывает по течению за 3 ч, а против течения реки – за 5 ч. Найдите собственную скорость лодки и скорость течения реки.Заранее спасибо, очень срочно нужно!!!

Answer 1

Vлодки-x
V течения- y
{3(x+y)=90
{5(x-y)=90
{3x+3y=90|*5
{5x-5y=90|*3
+{15x+15y=450
+{15x-15y=270
30x=720:30
x=24
3(24+y)=90
72+3y=90
3y=90-72
3y=18:3
y=6

Answer 2

Problem Analysis

We are given that the distance between two ports is 90 km. The boat takes 3 hours to travel this distance with the current and 5 hours to travel the same distance against the current. 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.

When the boat is traveling with the current, its effective speed is the sum of the boat's speed and the current's speed. So, the equation becomes: 90 = (B + C) × 3. When the boat is traveling against the current, its effective speed is the difference between the boat's speed and the current's speed. So, the equation becomes: 90 = (B - C) × 5. We can solve these two equations simultaneously to find the values of B and C.

Solving the Equations

Let's solve the equations using the substitution method.

From equation 1, we can express B in terms of C: B = 90/3 - C.

Substituting this value of B into equation 2, we get: 90 = (90/3 - C - C) × 5.

Simplifying the equation: 90 = (30 - 2C) × 5.

Expanding and rearranging the equation: 90 = 150 - 10C.

Solving for C: 10C = 150 - 90, 10C = 60, C = 6.

Substituting the value of C back into equation 1, we can find B: 90 = (B + 6) × 3.

Simplifying the equation: 90 = 3B + 18, 3B = 90 - 18, 3B = 72, B = 24.

Answer

Therefore, the speed of the boat is 24 km/h and the speed of the current is 6 km/h.

Please note that these calculations are based on the given information and assumptions made.