Question

Моторная лодка прошла 80 км по течению реки за 4 ч, а против течения реки - за 5ч. За сколько времени проплывет это же расстояние: А) плот по реке; Б) моторная лодка по озеру?

Answer 1

1) суммарная скорость лодки по течению реки v₁ = 80 : 4 = 20 (км/ч)
2) суммарная скорость лодки против течения реки v₂ = 80 : 5 = 16 (км/ч)
3) скорость лодки в стоячей воде: v = (v₁ + v₂) : 2 = 36 : 2 = 18 (км/ч)
    Скорость течения реки, таким образом, составит v₀ = 20 - 18 = 2 (км/ч)
4) Плот по реке проплывет за t₀ = S/v₀ = 80/2 = 40 (ч)
5) лодка по озеру проплывет за t = S/v = 80/18 = 4 4/9 (ч)

Answer 2

Calculation of Time for Different Scenarios

To calculate the time it takes to cover the same distance, we need to consider the speed of the boat and the speed of the current. Let's calculate the time for two scenarios: a raft floating downstream and a motorboat on a lake.

A) Raft Floating Downstream:

Given: - Distance: 80 km - Time taken downstream: 4 hours

To calculate the speed of the raft, we can divide the distance by the time taken downstream:

Speed of the raft downstream = Distance / Time taken downstream

Substituting the given values:

Speed of the raft downstream = 80 km / 4 hours = 20 km/h

Now, let's calculate the time it would take for the raft to cover the same distance upstream.

To calculate the time taken upstream, we can use the formula:

Time taken upstream = Distance / Speed of the raft upstream

Since the speed of the raft upstream is the difference between the speed of the raft and the speed of the current, we can calculate it as:

Speed of the raft upstream = Speed of the raft downstream - Speed of the current

Given that the time taken upstream is 5 hours, we can substitute the values into the formula:

Time taken upstream = 80 km / (Speed of the raft downstream - Speed of the current)

Substituting the known values:

5 hours = 80 km / (20 km/h - Speed of the current)

To solve for the speed of the current, we can rearrange the equation:

Speed of the current = 20 km/h - (80 km / 5 hours)

Simplifying:

Speed of the current = 20 km/h - 16 km/h = 4 km/h

Now that we know the speed of the current, we can calculate the speed of the raft upstream:

Speed of the raft upstream = Speed of the raft downstream - Speed of the current = 20 km/h - 4 km/h = 16 km/h

Finally, we can calculate the time taken for the raft to cover the same distance upstream:

Time taken upstream = Distance / Speed of the raft upstream = 80 km / 16 km/h = 5 hours

Therefore, it would take the raft 5 hours to cover the same distance upstream.

B) Motorboat on a Lake:

Given: - Distance: 80 km - Time taken downstream: 4 hours - Time taken upstream: 5 hours

Since the motorboat is on a lake, there is no current to consider. Therefore, the speed of the motorboat remains constant.

To calculate the speed of the motorboat, we can divide the distance by the time taken downstream:

Speed of the motorboat = Distance / Time taken downstream = 80 km / 4 hours = 20 km/h

Since the speed of the motorboat remains constant, it will take the same amount of time to cover the same distance upstream:

Time taken upstream = Distance / Speed of the motorboat = 80 km / 20 km/h = 4 hours

Therefore, it would take the motorboat 4 hours to cover the same distance upstream on a lake.

In summary: - The raft would take 5 hours to cover the same distance upstream. - The motorboat would take 4 hours to cover the same distance upstream on a lake.

Please note that these calculations assume a constant speed and do not take into account other factors such as wind or changes in water conditions.