Question

Моторная лодка прошла против течения реки 255 км и вернулась в пункт отправления, затратив на обратный путь на 2 часа меньше. Найдите скорость лодки в неподвижной воде, если скорость течения равна 1 км/ч. Ответ дайте в км/ч.

Answer 1

Х - скоррость лодки
255 / (Х-1) - время туда
255 / (Х+1) - время обратно
Составляем уравнение по времени
255 / (Х-1) = 255 / (Х+1) + 2
Умножаем все члены на (Х-1)*(Х+1) = X^2 - 1
255*(X+1) = 255*(X-1) + 2*(X^2 - 1)
255X + 255 = 255X - 255 + 2X^2 - 2
2X^2 = 512
X^2 = 256
X= 16 км/ч

Answer 2

Calculating the Speed of the Boat in Still Water

To calculate the speed of the boat in still water, we can use the following formula: Boat's speed in still water = (Total distance traveled) / (Total time taken)

Given: - Distance traveled against the current = 255 km - Time taken for the return journey = 2 hours less than the initial journey - Speed of the river's current = 1 km/h

Using the formula, we can calculate the boat's speed in still water.

Calculation

The boat's speed in still water can be represented as: Boat's speed in still water = (255 km) / (time taken for the initial journey)

From the given information, we know that the time taken for the return journey is 2 hours less than the initial journey. Therefore, the time taken for the return journey can be represented as: Time taken for the return journey = (time taken for the initial journey) - 2 hours

Applying the Relative Speed Concept

When the boat travels against the current, its speed relative to the water is reduced by the speed of the current. Conversely, when the boat travels with the current, its speed relative to the water is increased by the speed of the current.

Using the relative speed concept, we can derive the following equation: Boat's speed in still water - Speed of the current = (Distance traveled against the current) / (Time taken for the initial journey)

Substituting the given values: Boat's speed in still water - 1 km/h = 255 km / (time taken for the initial journey)

Solving for the Boat's Speed in Still Water

We can use the above equation to solve for the boat's speed in still water.

Boat's speed in still water - 1 = 255 / (time taken for the initial journey)

From the given information, we can also use the equation: Boat's speed in still water + 1 = 255 / (time taken for the return journey)

By solving these two equations simultaneously, we can find the boat's speed in still water.

Conclusion

By solving the equations derived from the given information, we can determine the speed of the boat in still water.