Question

15 б. срочно!умоляю!2 способа Решите задачу двумя способами. Решение обоснуйте. Катер проходит расстояние 210 км между двумя пристанями по течению за 5 ч, а против течения - за 6 ч. Найдите собственную скорость катера и скорость течения.

Answer 1

1 способ:
(x+y)*5=210 (x-y)*6=210 x+y=42 x-y=35 
2 способ:
210 +210= 420 км прошел катер за 5+6= 11 часов Причем, скорость реки была туда и обратно, получается, что она невилирует, т,е прибавляет 210км и убавляет 210км, ее нет! 420:11=41км в час

Answer 2

Problem Analysis

We are given that a boat travels a distance of 210 km between two piers. It takes 5 hours to travel downstream with the current and 6 hours to travel upstream against the current. We need to find the speed of the boat and the speed of the current.

Method 1: Using the Formula

One way to solve this problem is by using the formula for the speed of the boat in still water and the speed of the current.

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

When the boat is traveling downstream, the effective speed is the sum of the boat's speed and the current's speed. So, the effective speed is (x + y) km/h. According to the problem, it takes 5 hours to travel downstream, covering a distance of 210 km. We can use the formula distance = speed × time to write the equation:

210 = (x + y) × 5 Similarly, when the boat is traveling upstream, the effective speed is the difference between the boat's speed and the current's speed. So, the effective speed is (x - y) km/h. According to the problem, it takes 6 hours to travel upstream, covering the same distance of 210 km. We can use the same formula to write the equation:

210 = (x - y) × 6 Now, we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Method 2: Using Relative Speed

Another way to solve this problem is by using the concept of relative speed.

When the boat is traveling downstream, its speed relative to the water is x + y km/h. The distance traveled downstream is 210 km, and the time taken is 5 hours. We can use the formula distance = speed × time to write the equation:

210 = (x + y) × 5 Similarly, when the boat is traveling upstream, its speed relative to the water is x - y km/h. The distance traveled upstream is also 210 km, but the time taken is 6 hours. We can use the same formula to write the equation:

210 = (x - y) × 6 Again, we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Solving the System of Equations

Now, let's solve the system of equations using either method to find the values of x and y.

Using Method 1, we have the following equations: 210 = (x + y) × 5 210 = (x - y) × 6 Simplifying equation 210 = 5x + 5y

Simplifying equation 210 = 6x - 6y

Rearranging equation 6x - 6y = 210

Dividing both sides of equation by 6: x - y = 35 [[5]]

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