Question

Пристани а и в расстояние между которыми равно 120 км, расположены на реке,скорость течения которой на этом участке равна 5км/ч. Катер проходит от А до В и обратно без остановок со средней скоростью 24км/ч. Найдите собственную скорость катера

Answer 1

Средняя скорость выражается формулой

ср скорость=весь путь\всё время

24=240(так как туда и обратно)\x            x-в данном случае все время

x=240\24

x=10 часов

Теперь составим тождество где х скорость катера

120\(х+5)+120\(х-5)=10

(120х-600+120х+600)\х^2+25=10

240х\х^2+25=10

24х\х^2+25=1

24х=х^2+25

х^2-24х+25=0

D1=b\2+ac=144+25=169

x=12+-13

x=-1 b х=25

Ответ 25 км\ч

Answer 2

Calculation of the Boat's Speed

To find the boat's speed, we need to consider the speed of the current and the total distance traveled by the boat.

Given: - Distance between points A and B: 120 km - Speed of the current: 5 km/h - Average speed of the boat: 24 km/h

To calculate the boat's speed, we can use the formula:

Boat's speed = (Total distance traveled) / (Total time taken)

The total distance traveled by the boat is twice the distance between points A and B, as the boat travels from A to B and then back from B to A without any stops. Therefore, the total distance traveled is 2 * 120 km = 240 km.

To find the total time taken, we need to consider the effect of the current on the boat's speed. When the boat is traveling from A to B, it will have the current assisting its speed, and when it is traveling from B to A, it will have the current opposing its speed.

Let's calculate the time taken for each leg of the journey:

- Time taken from A to B: (Distance between A and B) / (Boat's speed + Speed of the current) - Time taken from B to A: (Distance between A and B) / (Boat's speed - Speed of the current)

Substituting the given values, we get:

- Time taken from A to B: 120 km / (24 km/h + 5 km/h) = 120 km / 29 km/h - Time taken from B to A: 120 km / (24 km/h - 5 km/h) = 120 km / 19 km/h

Now, we can calculate the total time taken:

- Total time taken = Time taken from A to B + Time taken from B to A

Substituting the calculated values, we get:

- Total time taken = (120 km / 29 km/h) + (120 km / 19 km/h)

To find the boat's speed, we can now use the formula mentioned earlier:

Boat's speed = (Total distance traveled) / (Total time taken)

Substituting the values, we get:

- Boat's speed = 240 km / ( (120 km / 29 km/h) + (120 km / 19 km/h) )

Now, let's calculate the boat's speed using the given values.