Question

Расстояние между двумя пунктами на реке 42 км на катере. Путь туда и обратно можно проделать за 3 часа 9 минут. Найди скорость катера в стоячей воде если скорость течения 3 км/ч

Answer 1

$\frac{42}{x+3} + \frac{42}{x-3} =3 \frac{9}{60} \\ \frac{42(x-3)+42(x+3)}{(x+3)(x-3)} =3 \frac{3}{20} \\ \frac{42x-126+42x+126}{x^2-9} = \frac{63}{20} \\63(x^2-9)=20*84x/:21\\3(x^2-9)=20*4x\\3x^2-27-80x=0\\ 3x^2-80x-27=0\\ D=80^2-4*3*(-27)=6724\\ \sqrt{D}=82\\x_{1,2}= \frac{80\pm82}{2*3} = \frac{80\pm82}{6} \\x_1=27\\x_2=- \frac{1}{3}$
Ответ: V=21 км/ч

Answer 2

Calculating the Boat's Speed in Still Water

To find the speed of the boat in still water, we can use the formula: Speed of boat in still water = (Speed downstream + Speed upstream) / 2

Given: - Distance between two points on the river = 42 km - Time taken for the round trip = 3 hours 9 minutes - Speed of the river's current = 3 km/h

First, let's calculate the speed of the boat downstream and upstream.

Calculating Speed Downstream

The speed downstream is the speed of the boat in still water added to the speed of the current. Speed downstream = Speed of boat in still water + Speed of current

Calculating Speed Upstream

The speed upstream is the speed of the boat in still water minus the speed of the current. Speed upstream = Speed of boat in still water - Speed of current

Now, we can use the given time and distance to calculate the speed of the boat in still water.

Calculation

Given: - Distance = 42 km - Time for round trip = 3 hours 9 minutes = 3.15 hours - Speed of current = 3 km/h

Using the formula: Speed of boat in still water = (Speed downstream + Speed upstream) / 2

We can calculate the speed of the boat in still water.