Question

Катер, двигаясь по течению проплывает от одной пристани до другой за 4 ч. Какое время затратит катер на обратный путь, если скорость течении 2 км.ч. а расстояние между пристанами равно 80 км. Скорость катера относительно воды считать постоянной. Плииз помогите!!!

Answer 1

Пусть
Х - скорость катера, тогда
Х+2 - скорость катера по течению
Так как S=v*t, то:
(X+2)*4=80
X=18 км/ч

На обратный путь катер поплывет против течения со скоростью Х-2, тогда время будет равно
t=s/(X-2)=80/16=5 часов

Answer 2

Problem Analysis

We are given the following information: - The boat is moving downstream from one dock to another in 4 hours. - The speed of the current is 2 km/h. - The distance between the docks is 80 km. - The speed of the boat relative to the water is constant.

We need to find the time it will take for the boat to return to the starting dock.

Solution

To solve this problem, we can use the concept of relative velocity. The boat's speed relative to the water is constant, so we can consider the boat's speed as the sum of its speed relative to the water and the speed of the current.

Let's assume the speed of the boat relative to the water is v km/h. Then, the speed of the boat downstream (with the current) is v + 2 km/h, and the speed of the boat upstream (against the current) is v - 2 km/h.

We can use the formula time = distance / speed to calculate the time it takes for the boat to travel between the docks.

Downstream Journey

For the downstream journey, the boat's speed is v + 2 km/h, and the distance is 80 km. Using the formula time = distance / speed, we can calculate the time it takes for the boat to travel downstream:

time_downstream = 80 / (v + 2) hours

Upstream Journey

For the upstream journey, the boat's speed is v - 2 km/h, and the distance is 80 km. Using the formula time = distance / speed, we can calculate the time it takes for the boat to travel upstream:

time_upstream = 80 / (v - 2) hours

Total Time

The total time for the round trip is the sum of the time taken for the downstream journey and the time taken for the upstream journey:

total_time = time_downstream + time_upstream hours Substituting the values of time_downstream and time_upstream from equations we get:

total_time = 80 / (v + 2) + 80 / (v - 2) hours

Now we can solve this equation to find the total time.

Calculation

Let's calculate the total time using the given values.

Substituting v = 4 km/h (speed of the boat relative to the water) into the equation, we get:

total_time = 80 / (4 + 2) + 80 / (4 - 2) hours

Simplifying the equation, we get:

total_time = 80 / 6 + 80 / 2 hours

Calculating the values, we get:

total_time = 13.33 + 40 hours

Therefore, the boat will take approximately 53.33 hours for the round trip.

Please note that the above calculation assumes that the boat maintains a constant speed relative to the water throughout the journey.

I hope this helps! Let me know if you have any further questions.