Question

Катер прошел 27 км по течению и 42 км против течения, затратив на путь по течению на 1 ч меньше, чем на путь против течения. Какова скорость катера против течения, если скорость течения реки равна 3 км/ч?

Answer 1

Пусть х км/ч скорость катера, тогда (х + 3) км/ч скорость катера плывшего по течению и (х-3) км/ч скорость катера плывшего против течения. Получаем:
42 / (х - 3) - 27 /(х+3) = 1. (42*(х+3)-27*(х-3))/((х-3)*(х+3))=1
42х+126-27х+81=х2-9 (х2 - это х в квадрате) решаем квадратное уравнение
х2 - 15х - 216 = 0; Д=225+864=1089.
х = 24 км/ч.
24 - 3 = 21 км/ч - скорость катера против течения

Answer 2

Problem Analysis

We are given that a boat traveled 27 km downstream and 42 km upstream. The time taken for the downstream journey was 1 hour less than the time taken for the upstream journey. We need to find the speed of the boat upstream, given that the speed of the river current is 3 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h. Since the boat is traveling downstream, its effective speed will be the sum of its speed in still water and the speed of the river current. Therefore, the effective speed downstream is (x + 3) km/h.

Similarly, when the boat is traveling upstream, its effective speed will be the difference between its speed in still water and the speed of the river current. Therefore, the effective speed upstream is (x - 3) km/h.

We are given that the time taken for the downstream journey is 1 hour less than the time taken for the upstream journey. Let's denote the time taken for the downstream journey as t hours. Therefore, the time taken for the upstream journey will be (t + 1) hours.

We can use the formula distance = speed × time to write the following equations:

For the downstream journey: 27 = (x + 3) × t For the upstream journey: **42 = (x - 3) ×