Question

Турист проплыл на байдарке 10 км против течения реки и 18 км по течению, затратив на весь путь столько же времени, сколько ему понадобилось бы, стобы проплыть по озеру 28 км. Зная, что скорость течения реки равна 2 км/ч, найдите собственную скорость байдарки.

Answer 1

Во вложениииииии..................

Answer 2

Problem Analysis

A tourist paddles a kayak for 10 km against the current of a river and then 18 km with the current. The time taken for this entire journey is the same as the time it would take to paddle 28 km on a lake. The speed of the river's current is given as 2 km/h. We need to find the speed of the kayak.

Solution

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

When the tourist paddles against the current, the effective speed of the kayak is reduced by the speed of the current. So, the speed of the kayak against the current is (x - 2) km/h.

When the tourist paddles with the current, the effective speed of the kayak is increased by the speed of the current. So, the speed of the kayak with the current is (x + 2) km/h.

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

Let's calculate the time taken to paddle against the current: - Distance = 10 km - Speed = (x - 2) km/h - Time = Distance / Speed = 10 / (x - 2) hours

Now, let's calculate the time taken to paddle with the current: - Distance = 18 km - Speed = (x + 2) km/h - Time = Distance / Speed = 18 / (x + 2) hours

According to the problem, the total time taken for the journey is the same as the time it would take to paddle 28 km on a lake. Let's calculate the time taken to paddle 28 km on a lake: - Distance = 28 km - Speed = x km/h (since there is no current in a lake) - Time = Distance / Speed = 28 / x hours

Since the total time taken for the journey is the same as the time taken to paddle 28 km on a lake, we can set up the following equation:

10 / (x - 2) + 18 / (x + 2) = 28 / x

Now, let's solve this equation to find the value of x, which represents the speed of the kayak in still water.

Solution Steps

1. Set up the equation: 10 / (x - 2) + 18 / (x + 2) = 28 / x 2. Multiply both sides of the equation by x(x - 2)(x + 2) to eliminate the denominators. 3. Simplify the equation and solve for x.

Let's solve the equation step by step:

1. Multiply both sides of the equation by x(x - 2)(x + 2): - x(x - 2)(x + 2) * (10 / (x - 2) + 18 / (x + 2)) = x(x - 2)(x + 2) * (28 / x) - 10x(x + 2) + 18x(x - 2) = 28(x - 2)(x + 2)

2. Simplify the equation: - 10x^2 + 20x + 18x^2 - 72x = 28(x^2 - 4) - 28x^2 - 52x = 28x^2 - 112

3. Cancel out the common terms: - 28x^2 - 28x^2 - 52x = -112 - -52x = -112

4. Solve for x: - x = -112 / -52 - x = 2.154

Therefore, the speed of the kayak in still water is approximately 2.154 km/h.

Answer

The speed of the kayak in still water is approximately 2.154 km/h.