Question

Катер шёл 3 часа по течению реки, затем на полчаса бросил якорь, затем полтора часа катер шёл по озеру. Собственная скорость катера 18 км/ч, скорость течения реки − 2 км/ч. Найдите среднюю скорость движения катера.

Answer 1

Ответ:

Введем переменную, пусть собственная

скорость катера равна х, значит, по озеру

катер шел со скоростью хкм/ч. А по течению

реки катер шел со скоростью (х+ З)км/ч

Зыразим время движения катера по теченикю

peки:t= S/;5/(x+ 3).

Выразим время движения катера по озеру:8/

X.

Так на все он потратил1 час, составляем

уравнение:

5/(x+3)+8/х=1;

(5x+8x+24x(x+3)=1;

(13х+24)/(x2+3x)=1.

По правилу пропорции:х2+ 3х=13х+ 24;

x2 + 3x- 13x-24= 0;

x2-10x-24=0

D-100+965196 (vD=14);

х1= (10-14)/2=-2 (не подходит)

х2 =(10 + 14)/2=12 (км/ч)- собственная

скорость катера.

Тогда скорость по течению будет равна х+3

-12+3=15 (km/4).

Ответ: скорость катера по течению равна 15

км/ч.

Answer 2

Problem Analysis

To find the average speed of the boat, we need to calculate the total distance traveled and the total time taken.

The boat traveled for 3 hours along the river, then anchored for 30 minutes, and finally traveled for 1.5 hours on the lake.

We know the boat's own speed is 18 km/h and the speed of the river's current is -2 km/h (negative because it's against the boat's direction).

Let's calculate the total distance and time traveled.

Calculation

The boat traveled at a speed of 18 km/h for 3 hours, so the distance traveled along the river is:

Distance along the river = Speed along the river * Time = (18 km/h - 2 km/h) * 3 hours = 16 km/h * 3 hours = 48 km

The boat then anchored for 30 minutes, which is 0.5 hours.

The boat traveled at a speed of 18 km/h for 1.5 hours on the lake, so the distance traveled on the lake is:

Distance on the lake = Speed on the lake * Time = 18 km/h * 1.5 hours = 27 km

The total distance traveled is the sum of the distances along the river and on the lake:

Total distance = Distance along the river + Distance on the lake = 48 km + 27 km = 75 km

The total time taken is the sum of the time spent along the river, the time spent anchoring, and the time spent on the lake:

Total time = Time along the river + Time anchoring + Time on the lake = 3 hours + 0.5 hours + 1.5 hours = 5 hours

Now we can calculate the average speed:

Average speed = Total distance / Total time = 75 km / 5 hours = 15 km/h

Answer

The average speed of the boat's movement is 15 km/h.