Question

От пристани А до пристани В лодка плыла по течению реки 3,5 ч. На обратный путь она затратила 5 ч 15 минут. Какое расстояние преодолела лодка за все время движения, если скорость течения реки 2 км/ч? Чуваки помогите:3

Answer 1

Она преодолела 16 ч и 20 минут

Answer 2

Problem Analysis

We are given that a boat traveled from port A to port B downstream in 3.5 hours and took 5 hours and 15 minutes to return upstream. We need to find the total distance the boat traveled during the entire journey, given that the river's current speed is 2 km/h.

Downstream Journey

During the downstream journey, the boat is moving in the same direction as the river's current. This means that the effective speed of the boat is the sum of its own speed and the speed of the current. Let's denote the boat's speed as B km/h and the speed of the current as C km/h.

The formula for calculating the effective speed during the downstream journey is:

Effective Speed = Boat's Speed + Current's Speed

In this case, the effective speed during the downstream journey is:

Effective Speed = B + C

We are given that the downstream journey took 3.5 hours. Using the formula for calculating distance, which is:

Distance = Speed × Time

we can calculate the distance traveled during the downstream journey as:

Distance Downstream = Effective Speed × Time Downstream

Substituting the values we have:

Distance Downstream = (B + C) × 3.5

Upstream Journey

During the upstream journey, the boat is moving against the direction of the river's current. This means that the effective speed of the boat is the difference between its own speed and the speed of the current.

The formula for calculating the effective speed during the upstream journey is:

Effective Speed = Boat's Speed - Current's Speed

In this case, the effective speed during the upstream journey is:

Effective Speed = B - C

We are given that the upstream journey took 5 hours and 15 minutes, which is equivalent to 5.25 hours. Using the formula for calculating distance, we can calculate the distance traveled during the upstream journey as:

Distance Upstream = Effective Speed × Time Upstream

Substituting the values we have:

Distance Upstream = (B - C) × 5.25

Total Distance

The total distance traveled by the boat during the entire journey is the sum of the distances traveled during the downstream and upstream journeys.

Total Distance = Distance Downstream + Distance Upstream

Substituting the values we calculated earlier:

Total Distance = (B + C) × 3.5 + (B - C) × 5.25

Now we can solve this equation to find the total distance traveled by the boat.

Solution

To find the total distance traveled by the boat, we need to solve the equation:

(B + C) × 3.5 + (B - C) × 5.25 = Total Distance

Given that the speed of the current is 2 km/h, we can substitute C = 2 into the equation:

(B + 2) × 3.5 + (B - 2) × 5.25 = Total Distance

Simplifying the equation:

3.5B + 7 + 5.25B - 10.5 = Total Distance

8.75B - 3.5 = Total Distance

Now we need to find the value of B that satisfies this equation.