Question

Моторная лодка прошла 28 км против течения реки и 16 км по течению, затратив на весь путь 3 ч. Какова скорость моторной лодки в стоячей воде, если известно, что скорость течения реки равна 1 км/ч?

Answer 1

V₁=v-1
v₂=v+1
16/(v+1)+28/(v-1)=3
16v-16+28v+28=3(v+1)(v-1)
44v+12=3(v²-v+v-1)
44v+12=3v²-3
3v²-44x-15=0
v₁=15
v₂=-1/3
Ответ: 15 км\ч

Answer 2

Calculating the Speed of the Motorboat

To calculate the speed of the motorboat in still water, we can use the following approach:

1. Let's denote the speed of the motorboat in still water as b and the speed of the river's current as c. 2. The time taken to travel 28 km against the current is 28 / (b - c). 3. The time taken to travel 16 km with the current is 16 / (b + c). 4. The total time taken for the entire journey is given as 3 hours.

Using the Given Information to Calculate the Speed

We can use the given information to set up the equation and solve for the speed of the motorboat in still water.

The equation can be set up as follows: 28 / (b - 1) + 16 / (b + 1) = 3

Solving for the Speed of the Motorboat

By solving the equation, we can find the speed of the motorboat in still water.

28 / (b - 1) + 16 / (b + 1) = 3 28(b + 1) + 16(b - 1) = 3(b^2 - 1) 28b + 28 + 16b - 16 = 3b^2 - 3 44b + 12 = 3b^2 - 3 3b^2 - 44b - 15 = 0

Using the quadratic formula: b = (-(-44) ± √((-44)^2 - 4*3*(-15))) / (2*3) b = (44 ± √(1936 + 180)) / 6 b = (44 ± √2116) / 6 b = (44 ± 46) / 6

The two possible solutions are: b = (44 + 46) / 6 = 90 / 6 = 15 b = (44 - 46) / 6 = -2 / 6 = -1/3

Since the speed of the motorboat cannot be negative, the speed of the motorboat in still water is 15 km/h. This is the valid solution for the speed of the motorboat in still water.

Therefore, the speed of the motorboat in still water is 15 km/h.