Question

По течению реки теплоход двигался со скоростью 15 км/ч, а против течения со скоростью 10 км/ч. С какой средней скоростью теплоход прошёл весь путь туда и обратно, если расстояние между двумя пристанями равно 8 км

Answer 1

Ответ: 25 километров в час

Answer 2

Problem Analysis

We are given the following information: - The speed of the boat downstream (with the current) is 15 km/h. - The speed of the boat upstream (against the current) is 10 km/h. - The distance between the two piers is 8 km.

We need to find the average speed of the boat for the entire round trip.

Solution

To find the average speed, we can use the formula:

Average Speed = Total Distance / Total Time

Let's calculate the total time for the round trip.

The time taken to travel downstream is given by:

Time Downstream = Distance Downstream / Speed Downstream

The time taken to travel upstream is given by:

Time Upstream = Distance Upstream / Speed Upstream

Since the distance downstream is the same as the distance upstream, we can write:

Distance Downstream = Distance Upstream = 8 km

Substituting the given values, we have:

Time Downstream = 8 km / 15 km/h

Time Upstream = 8 km / 10 km/h

To find the total time for the round trip, we add the time downstream and the time upstream:

Total Time = Time Downstream + Time Upstream

Now, we can substitute the values and calculate the total time.

Calculation

Time Downstream = 8 km / 15 km/h = 0.533 hours

Time Upstream = 8 km / 10 km/h = 0.8 hours

Total Time = 0.533 hours + 0.8 hours = 1.333 hours

Now, we can calculate the average speed using the formula:

Average Speed = Total Distance / Total Time

Substituting the values, we have:

Average Speed = 16 km / 1.333 hours

Answer

The average speed of the boat for the entire round trip is approximately 12 km/h.

Explanation

The average speed is calculated by dividing the total distance (which is twice the distance between the piers) by the total time taken for the round trip. In this case, the total distance is 16 km (8 km downstream + 8 km upstream) and the total time is 1.333 hours (0.533 hours downstream + 0.8 hours upstream). Dividing the total distance by the total time gives us the average speed of 12 km/h.