Question

Скорость катера относительно равна n км/ч,а скорость течения реки равна u км/ч.Расстояние между пристанями A и B равно 60км.Определитель время движения катера от A до B и обратно

Answer 1

Calculation of Time for Boat's Journey

To determine the time it takes for the boat to travel from point A to point B and back, we need to consider the speed of the boat and the speed of the river current.

Let's assume the speed of the boat is n km/h and the speed of the river current is u km/h. The distance between the two ports, A and B, is 60 km.

To calculate the time it takes for the boat to travel from A to B, we need to consider the combined effect of the boat's speed and the river current. When the boat is moving downstream (from A to B), the speed of the river current aids the boat's speed. Conversely, when the boat is moving upstream (from B to A), the speed of the river current opposes the boat's speed.

Time for Boat's Journey Downstream (from A to B)

When the boat is moving downstream, the effective speed of the boat is the sum of its own speed and the speed of the river current. Therefore, the boat's effective speed is (n + u) km/h.

To calculate the time it takes for the boat to travel from A to B downstream, we divide the distance between A and B by the effective speed of the boat:

Time Downstream = Distance / Effective Speed

Substituting the given values, we have:

Time Downstream = 60 km / (n + u) km/h

Time for Boat's Journey Upstream (from B to A)

When the boat is moving upstream, the effective speed of the boat is the difference between its own speed and the speed of the river current. Therefore, the boat's effective speed is (n - u) km/h.

To calculate the time it takes for the boat to travel from B to A upstream, we divide the distance between A and B by the effective speed of the boat:

Time Upstream = Distance / Effective Speed

Substituting the given values, we have:

Time Upstream = 60 km / (n - u) km/h

Total Time for Round Trip

To calculate the total time for the boat's round trip from A to B and back, we add the time it takes for the boat to travel downstream and the time it takes for the boat to travel upstream:

Total Time = Time Downstream + Time Upstream

Substituting the previously calculated values, we have:

Total Time = (60 km / (n + u) km/h) + (60 km / (n - u) km/h)

Please note that this calculation assumes a constant speed for the boat and the river current throughout the journey.

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