Question

Катер прошёл по реке от пристани А до пристани Б и вернулся назад.от А до Б катер шёл 2 ч.через 2.5 ч после выхода катера от пристани Б ему оставалось пройти до пристани А ещё 3 км.найдите расстояние между пристанями,если скорость течения реки 3 км/ч.

Answer 1

1) 60 : 30 = 2 часа 
1 час - 30 км\час
2 час - 30 км\час
3 час - 25 км\час
2) 45 : 22.5 = 2 часа
4 час - 22.5 км\час
5 час - 22.5 км\час
Средняя скорость теплохода равна:
( 30 + 30 + 25 + 22.5 + 22.5 ) \ 5 = 130 \ 5 = 26 ( км\час)
ОТВЕТ: 26 км\час

Answer 2

Calculation of the Distance Between the Docks

To find the distance between the docks, we need to consider the speed of the boat and the speed of the river current. Let's break down the information provided:

- The boat traveled from dock A to dock B in 2 hours. - After leaving dock B, the boat had to travel an additional 3 km to reach dock A. - The river current has a speed of 3 km/h.

To calculate the distance between the docks, we can use the formula:

Distance = Speed x Time

Let's calculate the time it took for the boat to travel from dock A to dock B, taking into account the river current:

- Boat speed = Boat speed - River current speed - Time = Distance / Speed

Using the given information, we can calculate the time it took for the boat to travel from dock A to dock B:

- Boat speed = Unknown (let's call it "x" km/h) - River current speed = 3 km/h - Time = 2 hours

2 hours = Distance / (Boat speed - River current speed)

Simplifying the equation, we have:

2 = Distance / (x - 3)

Now, let's calculate the time it took for the boat to travel from dock B back to dock A:

- Boat speed = Unknown (let's call it "y" km/h) - River current speed = 3 km/h - Time = 2.5 hours

2.5 hours = Distance / (y + 3)

Simplifying the equation, we have:

2.5 = Distance / (y + 3)

Finally, we know that after leaving dock B, the boat had to travel an additional 3 km to reach dock A. So, the total distance traveled by the boat is:

Total Distance = Distance + 3 km

Let's solve the system of equations to find the values of x, y, and the distance between the docks:

Solution:

To solve the system of equations, we can use substitution or elimination. Let's use substitution:

From the first equation, we have:

2 = Distance / (x - 3)

Rearranging the equation, we get:

Distance = 2(x - 3)

Substituting this value into the second equation, we have:

2.5 = (2(x - 3) + 3) / (y + 3)

Simplifying the equation, we get:

2.5 = (2x - 3 + 3) / (y + 3)

2.5 = (2x) / (y + 3)

Cross-multiplying, we have:

2.5(y + 3) = 2x

Simplifying further, we get:

2.5y + 7.5 = 2x

Now, let's substitute the value of Distance back into the equation:

Total Distance = Distance + 3

Total Distance = 2(x - 3) + 3

Simplifying, we have:

Total Distance = 2x - 3 + 3

Total Distance = 2x

Now, we have two equations:

2.5y + 7.5 = 2x (Equation 1)

Total Distance = 2x (Equation 2)

Since the total distance is the same as the distance traveled from dock A to dock B, we can equate Equation 1 and Equation 2:

2.5y + 7.5 = Total Distance

Substituting the value of Total Distance, we have:

2.5y + 7.5 = 2x

Now, we can solve this equation to find the value of y (the boat speed from dock B to dock A) in terms of x (the boat speed from dock A to dock B):

2.5y = 2x - 7.5

y = (2x - 7.5) / 2.5

Now, we can substitute this value of y back into Equation 1 to find the value of x:

2.5((2x - 7.5) / 2.5) + 7.5 = 2x

Simplifying the equation, we have:

2x - 7.5 + 7.5 = 2x

2x = 2x

This equation tells us that x can be any value. Therefore, the distance between the docks cannot be determined with the given information.

Please note that the calculation assumes a constant speed for the boat and the river current. Additionally, it assumes that the boat traveled at the same speed from dock A to dock B and from dock B back to dock A.