Question

Лодка проходит путь в 30 км по течению реки за 2 часа, а против течения реки за 3 часа. Найдите собственную скорость лодки и скорость течения реки подробное решение,СПАСИБО ЗАРАНЕЕ.

Answer 1

15 км он проходит в час по течению
10 км он проходит в час против течения
15-10=5км
5 длим на 2=2,5 км/ч течение
15-2,5=12,5 км в час собственная скорость
х+у=15
х-у=10      складываем равенства получим

2х=25
х=12.5-скорость лодки
15-12.5=2.5-- скорость течения

Answer 2

Problem Analysis

We are given that a boat travels a distance of 30 km downstream in 2 hours and the same distance upstream in 3 hours. We need to find the speed of the boat and the speed of the river current.

Solution

Let's assume the speed of the boat is B km/h and the speed of the river current is C km/h.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river current. Therefore, the boat's effective speed downstream is B + C km/h.

Similarly, when the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current. Therefore, the boat's effective speed upstream is B - C km/h.

We can use the formula speed = distance / time to calculate the boat's speed downstream and upstream.

Calculation

Given: - Distance downstream = 30 km - Time downstream = 2 hours - Distance upstream = 30 km - Time upstream = 3 hours

Using the formula speed = distance / time, we can calculate the boat's speed downstream and upstream:

- Speed downstream = Distance downstream / Time downstream = 30 km / 2 hours = 15 km/h - Speed upstream = Distance upstream / Time upstream = 30 km / 3 hours = 10 km/h

Now we have two equations: 1. B + C = 15 (equation 1) 2. B - C = 10 (equation 2)

We can solve these equations simultaneously to find the values of B and C.

Adding equation 1 and equation 2, we get: (B + C) + (B - C) = 15 + 10 2B = 25 B = 25 / 2 B = 12.5

Substituting the value of B into equation 1, we get: 12.5 + C = 15 C = 15 - 12.5 C = 2.5

Therefore, the speed of the boat is 12.5 km/h and the speed of the river current is 2.5 km/h.

Answer

The speed of the boat is 12.5 km/h and the speed of the river current is 2.5 km/h.

Verification

Let's verify our answer using the given information.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river current: 12.5 km/h + 2.5 km/h = 15 km/h

The distance downstream is 30 km, and the time taken is 2 hours: Speed downstream = Distance downstream / Time downstream = 30 km / 2 hours = 15 km/h

Similarly, when the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current: 12.5 km/h - 2.5 km/h = 10 km/h

The distance upstream is 30 km, and the time taken is 3 hours: Speed upstream = Distance upstream / Time upstream = 30 km / 3 hours = 10 km/h

Our calculated values match the given information, so our answer is correct.

Conclusion

The speed of the boat is 12.5 km/h and the speed of the river current is 2.5 km/h.