Question

Из двух пунктов реки, расстояние между которыми ровно 57 км, навстречу друг другу движутся две моторные лодки. Лодка идущая по течению реки , до встречи прошла 1 ч, а лодка , идущая против течения, 2 ч. Собственная скорость каждой из лодок равна 20 км.ч. Найдите скорость течения реки Заранее спасибо!

Answer 1

Х-скорость течения
(20+х)*1+(20-х)*2=57
20+х+40-2х=57
60-х=57
-х=57-60
-х=-3
х=3 км/ч

Answer 2

Problem Analysis

We are given two motorboats moving towards each other on a river. The distance between them is 57 km. One boat is moving downstream and takes 1 hour to meet the other boat, while the other boat is moving upstream and takes 2 hours to meet the first boat. The speed of each boat is 20 km/h. We need to find the speed of the river's current.

Solution

Let's assume the speed of the downstream boat is v1 and the speed of the upstream boat is v2. We are also given that the speed of each boat is 20 km/h.

According to the formula for relative speed, the speed at which the two boats are approaching each other is the sum of their individual speeds when moving towards each other, and the difference of their individual speeds when moving away from each other.

Using this formula, we can set up the following equations:

1. When the boats are moving towards each other: - v1 + v2 = 20 km/h 2. When the boats are moving away from each other: - v1 - v2 = 20 km/h We can solve these equations to find the values of v1 and v2.

Adding equation 1 and equation 2, we get: (v1 + v2) + (v1 - v2) = 20 + 20 2v1 = 40 v1 = 20 km/h

Substituting the value of v1 in equation 1, we get: 20 + v2 = 20 v2 = 0 km/h

Since the speed of the upstream boat is 0 km/h, it means that the boat is not moving against the current. Therefore, the speed of the river's current is 0 km/h.

Answer

The speed of the river's current is 0 km/h.