Question

Моторная лодка проехала 28 км против течения реки и 16 км по течению затратив на весь путь 3 ч .какова скорость моторной лодки в стоячей воде,если известна что скорость течения реки 1 км /ч

Answer 1

Скорость моторной лодки обозначим через Х. Тогда скорость по течению Х+1, а против течения - Х-1.
Время, затраченное на путь против течения, 28/(Х-1).
Время, затраченное на путь по течению, 16/(Х+1). Общее время - 3 ч. Составим уравнение
28/(Х-1)+16/(Х-1)=3.
 Если правильно его решишь, то получишь два корня Х1=15, и Х2=-1/3.
Ответ: 15 км/ч

Answer 2

Calculating the Speed of the Motorboat

To calculate the speed of the motorboat in still water, we can use the concept of relative speed. The speed of the motorboat in still water can be represented as the sum of its speed against the current and the speed of the current itself.

Given: - Distance traveled against the current = 28 km - Distance traveled with the current = 16 km - Total time taken = 3 hours - Speed of the current = 1 km/h

Calculating the Speed Against the Current

To calculate the speed of the motorboat against the current, we can use the formula: Speed = Distance / Time

The speed against the current can be calculated using the distance traveled against the current and the total time taken.

Using the given values: - Distance against the current = 28 km - Total time taken = 3 hours

We can calculate the speed against the current: Speed against the current = 28 km / 3 hours

Calculating the Speed With the Current

Similarly, to calculate the speed of the motorboat with the current, we can use the formula: Speed = Distance / Time

The speed with the current can be calculated using the distance traveled with the current and the total time taken.

Using the given values: - Distance with the current = 16 km - Total time taken = 3 hours

We can calculate the speed with the current: Speed with the current = 16 km / 3 hours

Calculating the Speed in Still Water

Now that we have the speed against the current and the speed with the current, we can calculate the speed of the motorboat in still water using the concept of relative speed.

The speed of the motorboat in still water can be calculated as: Speed in still water = (Speed with the current + Speed against the current) / 2

Using the calculated values: - Speed against the current = 28 km / 3 hours - Speed with the current = 16 km / 3 hours

We can calculate the speed of the motorboat in still water: Speed in still water = (28/3 + 16/3) / 2

Final Calculation

Let's calculate the final speed of the motorboat in still water: Speed in still water = (28/3 + 16/3) / 2 = (44/3) / 2 = 44/6 = 22/3 km/h

Therefore, the speed of the motorboat in still water is 22/3 km/h.