Question

Моторная лодка прошла 24 км против течения реки и 16 км по течению реки , затратив на весь путь 3 часа . НАйти собственную скорость лодки , если скорость течения реки 2 км/час . Как решить задачу подскажите пожалуйста

Answer 1

Х собственная скорость
х+2 скорость по течению
х-2 против течения
24/(х-2)+16/(х+2)=3
24х+48+16х-32=3х²-12
3х²-40х-28=0      D=1600+336=1936=44²
х=(40+44)/3=28км/час собственная скорость

Answer 2

Problem Analysis

We are given that a motorboat traveled 24 km against the current of a river and 16 km with the current of the river. The total time taken for the entire journey was 3 hours. The speed of the river's current is given as 2 km/h. We need to find the speed of the motorboat.

Solution

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

When the motorboat is traveling against the current, its effective speed is reduced by the speed of the current. So, the speed of the motorboat relative to the ground is (x - 2) km/h.

When the motorboat is traveling with the current, its effective speed is increased by the speed of the current. So, the speed of the motorboat relative to the ground is (x + 2) km/h.

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

The time taken to travel 24 km against the current is given by: 24 = (x - 2) × t1 (Equation 1)

The time taken to travel 16 km with the current is given by: 16 = (x + 2) × t2 (Equation 2)

We are also given that the total time taken for the entire journey is 3 hours: t1 + t2 = 3 (Equation 3)

We can solve this system of equations to find the value of x.

Solution Steps

1. Rearrange Equation 1 to solve for t1: t1 = 24 / (x - 2)

2. Rearrange Equation 2 to solve for t2: t2 = 16 / (x + 2)

3. Substitute the values of t1 and t2 into Equation 3: 24 / (x - 2) + 16 / (x + 2) = 3

4. Multiply both sides of the equation by (x - 2)(x + 2) to eliminate the denominators: 24(x + 2) + 16(x - 2) = 3(x - 2)(x + 2)

5. Simplify and expand the equation: 24x + 48 + 16x - 32 = 3(x^2 - 4)

6. Simplify further: 40x + 16 = 3x^2 - 12

7. Rearrange the equation to form a quadratic equation: 3x^2 - 40x - 28 = 0

8. Solve the quadratic equation using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / (2a)

where a = 3, b = -40, and c = -28.

Plugging in the values: x = (-(-40) ± sqrt((-40)^2 - 4 * 3 * (-28))) / (2 * 3)

Simplifying: x = (40 ± sqrt(1600 + 336)) / 6

x = (40 ± sqrt(1936)) / 6

x = (40 ± 44) / 6

So, we have two possible solutions for x: x1 = (40 + 44) / 6 = 14 km/h x2 = (40 - 44) / 6 = -1 km/h

Since the speed of the motorboat cannot be negative, the speed of the motorboat is 14 km/h.

Answer

The speed of the motorboat is 14 km/h.