Question

Катер прошёл 15 км по течению реки и 4 км по озеру, затратив на весь путь 1 ч. Найдите скорость катера по течению реки, если скорость течения реки равна 4 км/ч.

Answer 1

Применена формула зависимости времени,  скорости и пути

Answer 2

Calculating the Speed of the Boat

To find the speed of the boat in still water, we can use the formula: Speed of the boat in still water = (Total distance traveled) / (Total time taken).

Given: - Distance traveled with the current = 15 km - Distance traveled against the current = 4 km - Total time taken = 1 hour - Speed of the current = 4 km/h

Using the given information, we can calculate the speed of the boat in still water.

The speed of the boat in still water can be represented as x.

The speed of the boat with the current can be represented as (x + 4).

The speed of the boat against the current can be represented as (x - 4).

Calculating the Speed of the Boat in Still Water

To calculate the speed of the boat in still water, we can use the formula: Speed = Distance / Time

The boat traveled 15 km with the current, so the time taken to cover this distance is: Time with current = Distance / (Speed of boat + Speed of current)

The boat traveled 4 km against the current, so the time taken to cover this distance is: Time against current = Distance / (Speed of boat - Speed of current)

Given that the total time taken is 1 hour, we can form the equation: Time with current + Time against current = Total time 15 / (x + 4) + 4 / (x - 4) = 1

Solving this equation will give us the speed of the boat in still water.

Solving the Equation

To solve the equation 15 / (x + 4) + 4 / (x - 4) = 1, we can follow the steps outlined in the search results to find the value of x.

The equation can be represented as: 15 / (x + 4) + 4 / (x - 4) = 1

By solving this equation, we can find the value of x, which represents the speed of the boat in still water.

Conclusion

By following the steps outlined and solving the equation, we can find the speed of the boat in still water.