Question

Лодка прошла от одного селения до другого против течения за 3 часа, на обратный путь затратила 2 часа. Скорость течения реки 3 км/ч. Найти собственную скорость лодки и расстояние между селениями

Answer 1

скорость лодки х. тогда скорость против течения х-3 за 3 часа расстояние равно 3х-9. делим на скорость по течению х+3 и получим 2 часа.

3х-9/х+3=2

3х-9=2х+6

х=9+6

х=15 км/час расстояние равно ( 15+3)*2=36км

ответ скорость катера 15 км/час , а расстояние между селами 36 км

Answer 2

Problem Analysis

We are given that a boat traveled from one village to another against the current of a river in 3 hours, and it took 2 hours for the return journey. The speed of the river current is given as 3 km/h. We need to find the speed of the boat and the distance between the villages.

Solution

Let's assume the speed of the boat is B km/h and the distance between the villages is D km.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the boat's speed relative to the ground is B - 3 km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the boat's speed relative to the ground is B + 3 km/h.

We can use the formula speed = distance / time to calculate the speed, and rearrange it to find the distance.

Calculation

Let's calculate the speed of the boat and the distance between the villages.

1. When the boat is traveling against the current: - Speed of the boat relative to the ground: B - 3 km/h - Time taken: 3 hours - Distance traveled: (B - 3) * 3 km

2. When the boat is traveling with the current: - Speed of the boat relative to the ground: B + 3 km/h - Time taken: 2 hours - Distance traveled: (B + 3) * 2 km

Since the distance traveled in both cases is the same (from one village to another and back), we can equate the distances and solve for B and D.

Equation 1: (B - 3) * 3 = (B + 3) * 2

Simplifying Equation 1: 3B - 9 = 2B + 6 B = 15