Question

Моторная лодка шла от A до B по течению реки 3 часа, а от В до А - 5 часов. Скорость течения равна 3 км/ч. Найдите скорость лодки в стоячей воде и расстояние от А до В

Answer 1

Принимаем скорость в стоячей воде за х и составляем уравнение. находим х и находим расстояние от а до в

Answer 2

Problem Analysis

We are given that a motorboat traveled from point A to point B downstream in 3 hours, and from point B to point A upstream in 5 hours. The speed of the river current is given as 3 km/h. We need to find the speed of the boat in still water and the distance between points A and B.

Solution

Let's assume the speed of the boat in still water is v km/h.

When the boat is traveling downstream from A to B, it is moving with the current, so the effective speed is the sum of the boat's speed and the current's speed. Therefore, the boat's speed downstream is v + 3 km/h.

When the boat is traveling upstream from B to A, it is moving against the current, so the effective speed is the difference between the boat's speed and the current's speed. Therefore, the boat's speed upstream is v - 3 km/h.

We can use the formula distance = speed × time to calculate the distance between points A and B.

Let's denote the distance between A and B as d km.

From the given information, we have the following equations:

1. Downstream journey: d = (v + 3) × 3 (since