Question

Расстояние между пунктами А и В равно 48км. Моторная лодка проплыла из А в В и обратно, затратив на весь путь 5 часов. Найти скорость течения если собственная скорость 20 км/x

Answer 1

Пошаговое объяснение:

ответ 4 км/ч

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Answer 2

Ответ:

3 х - собственная скорость лодки х+4 - скорость по течению

х-4 - скорость против течения

48/(х+4) - время движения по течению 48/(х-4) - время против течения 48/(х+4)+48/(х-4)=5 (умножим на (х+4) (х-4)) 48(х-4)+48(х+4)=5(х-4)(х+4) 48х-192+48х+192=5(Х2+4х-4х-16) 96x с=5х2-80 5х2-96x с-80=0 д=96*96-4*5(-80)=9216+1600=10816 корень из Д=104 х(1)=(96-104):2*5=-8:10=-4/5 (не подходит по условию) х(2)=(96+104):2*5=200:10=20 (км/ч) ответ:собственная скорость равна 20 км/ч главный насколько

Answer 3

Problem Analysis

We are given that the distance between points A and B is 48 km. A motorboat traveled from A to B and back, taking a total of 5 hours for the entire journey. We need to find the speed of the current if the boat's own speed is 20 km/h.

Solution

Let's assume the speed of the current is x km/h.

The boat's speed relative to the water is the sum of its own speed and the speed of the current when traveling downstream, and the difference when traveling upstream.

When traveling downstream from A to B, the boat's speed is 20 + x km/h. The time taken for this leg of the journey is 48 / (20 + x) hours.

When traveling upstream from B to A, the boat's speed is 20 - x km/h. The time taken for this leg of the journey is 48 / (20 - x) hours.

The total time taken for the entire journey is given as 5 hours. Therefore, we can write the equation:

48 / (20 + x) + 48 / (20 - x) = 5

To solve this equation, we can multiply through by the denominators to eliminate the fractions:

48(20 - x) + 48(20 + x) = 5(20 + x)(20 - x)

Simplifying the equation:

960 - 48x + 960 + 48x = 400 - x^2

1920 = 400 - x^2

x^2 = 1520

Taking the square root of both sides:

x = √1520

Evaluating the square root:

x ≈ 38.98 km/h

Therefore, the speed of the current is approximately 38.98 km/h.

Answer

The speed of the current is approximately 38.98 km/h.