Question

моторная лодка двигаясь против течения реки прошла расстояние от турбазы до города за 3 часа,а обратный путь-за 2 часа 15 минут.скорость течения реки равна 4 км/ч...какова собственная скорость катера?Помогите пожалуйста)))

Answer 1

(x-4)*3=(x+4)*2,25

3x-12=2.25x+9

0.75x=21

x=28

otvet: 28

Answer 2

Calculation of the Boat's Speed

To determine the boat's speed, we need to calculate the distance traveled and the time taken for both the upstream and downstream journeys.

Given information: - Time taken for the upstream journey: 3 hours - Time taken for the downstream journey: 2 hours 15 minutes (or 2.25 hours) - Speed of the river's current: 4 km/h

Let's denote the boat's speed as x km/h.

Upstream Journey

During the upstream journey, the boat is moving against the current of the river. This means that the effective speed of the boat is reduced by the speed of the current.

The distance traveled during the upstream journey is the same as the distance from the tourist base to the city.

Using the formula distance = speed × time, we can calculate the distance traveled during the upstream journey:

distance = (x - 4) km/h × 3 hours

Downstream Journey

During the downstream journey, the boat is moving with the current of the river. This means that the effective speed of the boat is increased by the speed of the current.

The distance traveled during the downstream journey is also the same as the distance from the tourist base to the city.

Using the same formula, we can calculate the distance traveled during the downstream journey:

distance = (x + 4) km/h × 2.25 hours

Equating the Distances

Since the distance traveled is the same for both the upstream and downstream journeys, we can equate the two distances:

(x - 4) km/h × 3 hours = (x + 4) km/h × 2.25 hours

Now, let's solve this equation to find the value of x, which represents the boat's speed.

Solving the Equation

To solve the equation, we can start by simplifying it:

3(x - 4) = 2.25(x + 4)

Expanding the equation:

3x - 12 = 2.25x + 9

Combining like terms:

3x - 2.25x = 9 + 12

Simplifying further:

0.75x = 21

Dividing both sides by 0.75:

x = 28

Therefore, the boat's speed is 28 km/h.

Conclusion

The boat's speed is 28 km/h. This calculation is based on the given information about the time taken for the upstream and downstream journeys and the speed of the river's current.

Please note that this calculation assumes a constant speed throughout the journey and does not account for other factors such as wind or variations in the river's current.