Question

Лодка прошла по течению реки 75 км, затем повернула в обратную сторону и прошла 45 км против течения, затратив на весь путь 10 часов. Найди собственную скорость лодки, если скорость течения равна 3 км/ч.​

Answer 1

Ответ:

12км/ч

Пошаговое объяснение:

75/(x+3)+45/(x-3)=10

75x-225+45x+135=10x²-90

10x²-120x=0

x1=12 x2=0 (отбрасываем, т.к. неудовлетворяет условию задачи (с ним время назад отрицательное))

Answer 2

Problem Analysis

We are given that a boat traveled downstream on a river for 75 km, then turned around and traveled upstream for 45 km against the current. The total time taken for the entire journey was 10 hours. We need to find the speed of the boat.

Downstream Speed

Let's assume the speed of the boat in still water is x km/h and the speed of the current is 3 km/h. When the boat is traveling downstream, it gets an additional boost from the current, so its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's speed downstream is (x + 3) km/h.

Upstream Speed

When the boat is traveling upstream against the current, it has to overcome the resistance of the current. So its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's speed upstream is (x - 3) km/h.

Time Calculation

We are given that the boat traveled 75 km downstream and 45 km upstream, and the total time taken for the entire journey was 10 hours. We can use the formula time = distance / speed to calculate the time taken for each leg of the journey.

The time taken to travel downstream is 75 / (x + 3) hours.

The time taken to travel upstream is 45 / (x - 3) hours.

The sum of these two times should be equal to 10 hours:

(75 / (x + 3)) + (45 / (x - 3)) = 10

Solving the Equation

To solve the equation, we can multiply both sides by (x + 3)(x - 3) to eliminate the denominators:

(75(x - 3)) + (45(x + 3)) = 10(x + 3)(x - 3)

Simplifying the equation:

75x - 225 + 45x + 135 = 10(x^2 - 9)

120x - 90 = 10x^2 - 90

10x^2 - 120x = 0

Dividing both sides by 10x:

x - 12 = 0

x = 12

Answer

The speed of the boat in still water is 12 km/h.

Verification

Let's verify our answer by substituting the value of x into the equation:

(75 / (12 + 3)) + (45 / (12 - 3)) = 10

75 / 15 + 45 / 9 = 10

5 + 5 = 10

The equation holds true, so our answer is correct.