Question

За 5 часов лодка проплыла против течения на 65 км меньше, чем за 7 часов по течению. Скорость лодки против течения составляет 75% скорости лодки по течению. Определите собственную скорость лодки

Answer 1

Скорость лодки х, скорость течения у.
Х-y = 75(x+y)/100=3(x+y)/4, 4(x-у)-3(x+У)=0; 7((х+y)-5(х-у)=65; х+у=20, х-у=15;
Х=17.5;

Answer 2

Calculation of the Boat's Speed

To determine the boat's speed, we can use the information provided in the question. Let's break down the given information:

- The boat traveled a certain distance against the current in 5 hours. - The boat traveled the same distance with the current in 7 hours. - The speed of the boat against the current is 75% of the speed of the boat with the current.

Let's denote the speed of the boat as x km/h and the speed of the current as y km/h.

To calculate the boat's speed, we can set up the following equations:

1. Against the current: Distance = Speed × Time - Distance = (x - y) km/h × 5 hours - Distance = 5(x - y) km

2. With the current: Distance = Speed × Time - Distance = (x + y) km/h × 7 hours - Distance = 7(x + y) km

According to the given information, the boat traveled 65 km less against the current than with the current. Therefore, we can set up the following equation:

3. Against the current distance = With the current distance - 65 km - 5(x - y) = 7(x + y) - 65

Now, let's solve this equation to find the boat's speed.

Solving the Equation

To solve the equation, we'll start by expanding the equation:

5x - 5y = 7x + 7y - 65

Next, we'll simplify the equation by combining like terms:

-2x - 12y = -65

Now, let's isolate x by moving the terms involving y to the other side of the equation:

-2x = 12y - 65

Finally, we'll solve for x by dividing both sides of the equation by -2:

x = (12y - 65) / -2

Now we have the equation for the boat's speed x in terms of the current speed y.

Conclusion

The equation for the boat's speed x in terms of the current speed y is:

x = (12y - 65) / -2

Please note that this equation gives the relationship between the boat's speed and the current speed. To determine the specific values, we would need additional information or values for the current speed.