Question

2. Моторная лодка прошла 20 км против течения реки и 18 км по течению, затратив на весь путь 2 ч. Найдите скорость лодки в стоячей воде, если скорость течения реки равна 4 км/ч. СРОЧНООООО ДАЮ 50​

Answer 1

Ответ:

ошибка в условии задачи

Объяснение:

Пусть собственная скорость лодки х км/ч, тогда её скорость по течению х+4 км/ч, против течения х-4 км/ч.

20/(х-4) + 18/(х+4) = 2

20х+80+18х-72-2х²+32=0

х²-19х+12=0

D=b²-4ac=361-48=313;

проверьте условие задачи

Answer 2

Problem Analysis

We are given that a motorboat traveled 20 km against the current of a river and 18 km with the current, taking a total of 2 hours for the entire journey. We need to find the speed of the boat in still water, given that the speed of the river current is 4 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the boat's speed against the current is (x - 4) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the boat's speed with the current is (x + 4) km/h.

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

The time taken to travel 20 km against the current is given by: 20 = (x - 4) × t1 The time taken to travel 18 km with the current is given by: 18 = (x + 4) × t2 We are also given that the total time for the journey is 2 hours: t1 + t2 = 2 We can solve this system of equations to find the value of x, the speed of the boat in still water.

Solution Steps

1. Rearrange equation to solve for t1: t1 = 20 / (x - 4)

2. Rearrange equation to solve for t2: t2 = 18 / (x + 4)

3. Substitute the values of t1 and t2 into equation 20 / (x - 4) + 18 / (x + 4) = 2

4. Multiply both sides of the equation by (x - 4)(x + 4) to eliminate the denominators: 20(x + 4) + 18(x - 4) = 2(x - 4)(x + 4)

5. Simplify and solve the resulting quadratic equation for x.

Let's solve the equation step by step:

Solution Steps

1. Rearrange equation to solve for t1: t1 = 20 / (x - 4)

2. Rearrange equation to solve for t2: t2 = 18 / (x + 4)

3. Substitute the values of t1 and t2 into equation 20 / (x - 4) + 18 / (x + 4) = 2

4. Multiply both sides of the equation by (x - 4)(x + 4) to eliminate the denominators: 20(x + 4) + 18(x - 4) = 2(x - 4)(x + 4)

5. Simplify and solve the resulting quadratic equation for x.

Let's solve the equation step by step:

Solution Steps

1. Rearrange equation to solve for t1: t1 = 20 / (x - 4)

2. Rearrange equation to solve for t2: t2 = 18 / (x + 4)

3. Substitute the values of t1 and t2 into equation 20 / (x - 4) + 18 / (x + 4) = 2

4. Multiply both sides of the equation by (x - 4)(x + 4) to eliminate the denominators: 20(x + 4) + 18(x - 4) = 2(x - 4)(x + 4)

5. Simplify and solve the resulting quadratic equation for x.

Let's solve the equation step by step:

Solution Steps

1. Rearrange equation to solve for t1: t1 = 20 / (x - 4)

2. Rearrange equation to solve for t2: t2 = 18 / (x + 4)

3. Substitute the values of t1 and t2 into equation 20 / (x - 4) + 18 / (x + 4) = 2

4. Multiply both sides of the equation by (x - 4)(x + 4) to eliminate the denominators: 20(x + 4) + 18(x - 4) = 2(x - 4)(x + 4)

5. Simplify and solve the resulting quadratic equation for x.

Let's solve the equation step by step:

Solution Steps

1. Rearrange equation to solve for t1: t1 = 20 / (x - 4)

2. Rearrange equation to solve for t2: t2 = 18 / (x + 4)

3. Substitute the values of t1 and t2 into equation 20 / (x - 4) + 18 / (x + 4) = 2

4. Multiply both sides of the equation by (x - 4)(x + 4) to eliminate the denominators: 20(x + 4) + 18(x - 4) = 2(x - 4)(x + 4)

5. Simplify and solve the resulting quadratic equation for x.

Let's solve the equation step by step:

Solution Steps

1. Rearrange equation to solve for t1: t1 = 20 / (x - 4)

2. Rearrange equation to solve for t2: t2 = 18 / (x + 4)

3. Substitute the values of t1 and t2 into equation 20 / (x - 4) + 18 / (x + 4) = 2

4. Multiply both sides of the equation by (x - 4)(x + 4) to eliminate the denominators: 20(x + 4) + 18(x - 4) = 2(x - 4)(x + 4)

5. Simplify and solve the resulting quadratic equation for x.

Let's solve the equation step by step:

Solution Steps

1. Rearrange equation to solve for t1: t1 = 20 / (x - 4)

2. Rearrange equation to solve for t2: t2 = 18 / (x + 4)

3. Substitute the values of t1 and t2 into equation 20 / (x - 4) + 18 / (x + 4) = 2

4. Multiply both sides of the equation by (x - 4)(x + 4) to eliminate the denominators: 20(x + 4) + 18(x - 4) = 2(x - 4)(x + 4)

5. Simplify and solve the resulting quadratic equation for x.

Let's solve the equation step by step:

Solution Steps

1. Rearrange equation to solve for t1: t1 = 20 / (x - 4)

2. Rearrange equation to solve for t2: t2 = 18 / (x + 4)

3. Substitute the values of t1 and t2 into equation 20 / (x - 4) + 18 / (x + 4) = 2

4. Multiply both sides of the equation by (x - 4)(x + 4) to eliminate the denominators: 20(x + 4) + 18(x - 4) = 2(x - 4)(x + 4)

5. Simplify and solve the resulting quadratic equation for x.

Let's solve the equation step by step:

Solution Steps

1. Rearrange equation to solve for t1: t1 = 20 / (x - 4)

2. Rearrange equation to solve for t2: t2 = 18 / (x + 4)

3. Substitute the values of t1 and t2 into equation 20 / (x - 4) + 18 / (x + 4) = 2

4. Multiply both sides of the equation by (x - 4)(x + 4) to eliminate the denominators: 20(x + 4) + 18(x - 4) = 2(x - 4)(x + 4)

5. Simplify and solve the resulting quadratic equation for x.

Let's solve the equation step by step:

Solution Steps

1. Rearrange equation to solve for **