Question

катер за 3 часа по течению и 5 ч против течения проходит 76км найдите скорость течения и собственную скорость катера если за 6ч по течению катер проходит столько же сколько за 9 часов против течения

Answer 1

6(х+у)=9(х-у)

3(х+у)+5(х-у)=76

 

2х+2у=3х-3у

3х+3у+5х-5у=76

5у=х

8х-2у=76

х=5у

4х-у=38

20у-у=38

19у=38

у=2

х=10

10 км/ч скорость катера

2 км/ч скорость течения

Answer 2

вот... с решением.... если че то не понятно, отпишись мне...

 

Answer 3

Problem Analysis

We are given that a boat travels 76 km in 3 hours with the current and in 5 hours against the current. We need to find the speed of the current and the speed of the boat in still water. Additionally, we are given that the boat travels the same distance in 6 hours with the current as it does in 9 hours against the current.

Solution

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 with the current, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the boat's effective speed is (x + y) km/h.

When the boat is traveling against the current, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the boat's effective speed is (x - y) km/h.

We can set up the following equations based on the given information:

1. When the boat is traveling with the current: - Distance = Speed × Time - 76 km = (x + y) km/h × 3 hours 2. When the boat is traveling against the current: - Distance = Speed × Time - 76 km = (x - y) km/h × 5 hours 3. The boat travels the same distance in 6 hours with the current as it does in 9 hours against the current: - Distance = Speed × Time - (x + y) km/h × 6 hours = (x - y) km/h × 9 hours We can solve this system of equations to find the values of x and y.

Solution Steps

1. Start with equation 1: 76 km = (x + y) km/h × 3 hours. 2. Divide both sides of the equation by 3 to isolate (x + y): (x + y) km/h = 76 km / 3 hours. 3. Simplify the right side of the equation: (x + y) km/h = 25.33 km/h. 4. Now, we have the value of (x + y). We can substitute this value into equation 3: 25.33 km/h × 6 hours = (x - y) km/h × 9 hours. 5. Simplify the equation: 152 km = 9(x - y) km/h × hours. 6. Divide both sides of the equation by 9 hours to isolate (x - y): (x - y) km/h = 152 km / 9 hours. 7. Simplify the right side of the equation: (x - y) km/h = 16.89 km/h. 8. Now, we have the values of (x + y) and (x - y). We can solve these two equations simultaneously to find the values of x and y. 9. Add equation 1 and equation 2: (x + y) km/h + (x - y) km/h = 25.33 km/h + 16.89 km/h. 10. Simplify the equation: 2x km/h = 42.22 km/h. 11. Divide both sides of the equation by 2 to isolate x: x km/h = 42.22 km/h / 2. 12. Simplify the right side of the equation: x km/h = 21.11 km/h. 13. Now, we have the value of x. We can substitute this value into equation 1 to find the value of y: 76 km = (21.11 km/h + y) km/h × 3 hours. 14. Divide both sides of the equation by 3 hours to isolate (21.11 km/h + y): (21.11 km/h + y) km/h = 76 km / 3 hours. 15. Simplify the right side of the equation: (21.11 km/h + y) km/h = 25.33 km/h. 16. Subtract 21.11 km/h from both sides of the equation to isolate y: y km/h = 25.33 km/h - 21.11 km/h. 17. Simplify the right side of the equation: y km/h = 4.22 km/h.

Answer

The speed of the current is 4.22 km/h and the speed of the boat in still water is 21.11 km/h.

Explanation

According to the given information, the boat travels 76 km in 3 hours with the current and 76 km in 5 hours against the current. By solving the system of equations, we found that the speed of the current is 4.22 km/h and the speed of the boat in still water is 21.11 km/h.