Question

Катер проплыл 18 км по течению реки и 24 кмпротив течения,потратив на весь путь 3ч,найдите скорость течения реки ,если собственная скорость катера 15км/ч ПОМОГИТЕ ПОЖАЛУЙСТА!!!!!!!!!!!!!

Answer 1

Решение во вложении. Удачи

Answer 2

Problem Analysis

We are given that a boat traveled 18 km downstream (with the current) and 24 km upstream (against the current) in a total of 3 hours. We need to find the speed of the river's current.

Solution

Let's assume the speed of the river's current is x km/h. The boat's speed in still water is given as 15 km/h.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's speed downstream is 15 + x km/h.

Similarly, when the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's speed upstream is 15 - x km/h.

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

1. Downstream journey: - Distance: 18 km - Speed: 15 + x km/h - Time: 18 / (15 + x) hours 2. Upstream journey: - Distance: 24 km - Speed: 15 - x km/h - Time: 24 / (15 - x) hours The total time for the entire journey is given as 3 hours. Therefore, the sum of the times for the downstream and upstream journeys should be equal to 3 hours:

18 / (15 + x) + 24 / (15 - x) = 3

To solve this equation, we can multiply both sides by (15 + x)(15 - x) to eliminate the denominators:

18(15 - x) + 24(15 + x) = 3(15 + x)(15 - x)

Simplifying the equation:

270 - 18x + 360 + 24x = 45(15^2 - x^2)

Combining like terms:

630 = 45(225 - x^2)

Dividing both sides by 45:

14 = 225 - x^2

Rearranging the equation:

x^2 = 225 - 14

x^2 = 211

Taking the square root of both sides:

x = √211

Therefore, the speed of the river's current is approximately √211 km/h.

Answer

The speed of the river's current is approximately √211 km/h.