Question

Расстояние от A до B =45 км. Из А в В отправился плот, через час вслед за ним моторная лодка, которая, прибыв в В, тотчас вернулась назад в пункт А. К этому времени плот проплыл 28 км. Найти скорость лодки в стоячей воде, если скорость течения реки =4 км/ч

Answer 1

Пусть скорость лодки в стоячей воде v км/ч, тогда:
28/4 - 1 = 6 часов плыла лодка
45/(v+4) + 45/(v-4) = 6
45 * 2v / (v^2 - 16) = 6
v^2 - 16 = 15v
v^2 - 15v -16 = 0
(v+1)(v-16) = 0
v = 16
Ответ: 16 км/ч

Answer 2

Problem Analysis

We are given the following information: - The distance from point A to point B is 45 km. - A raft started from point A and after one hour, a motorboat followed it from point A to point B. The motorboat immediately returned to point A upon reaching point B. - By the time the motorboat returned to point A, the raft had traveled 28 km. - The speed of the river current is 4 km/h.

We need to find the speed of the motorboat in still water.

Solution

Let's assume the speed of the motorboat in still water is x km/h.

Since the raft traveled 28 km in the time it took for the motorboat to travel from point A to point B and back, we can calculate the time it took for the motorboat to travel from point A to point B and back using the formula:

time = distance / speed

The time taken by the motorboat to travel from point A to point B and back is given by:

time = (45 km) / (x km/h)

The time taken by the raft to travel 28 km is given by:

time = (28 km) / (x km/h + 4 km/h)

Since both times are equal, we can set up the following equation:

(45 km) / (x km/h) = (28 km) / (x km/h + 4 km/h)

Now, we can solve this equation to find the value of x.

Calculation

Let's solve the equation:

(45 km) / (x km/h) = (28 km) / (x km/h + 4 km/h)

Cross-multiplying the equation:

(45 km) * (x km/h + 4 km/h) = (28 km) * (x km/h)

Expanding the equation:

(45 km) * x km/h + (45 km) * 4 km/h = (28 km) * x km/h

Simplifying the equation:

(45x + 180) km²/h = (28x) km²/h

Now, let's solve for x:

(45x + 180) = (28x)

Expanding the equation:

45x + 180 = 28x

Subtracting 28x from both sides:

45x - 28x + 180 = 0

Simplifying the equation:

17x + 180 = 0

Subtracting 180 from both sides:

17x = -180

Dividing both sides by 17:

x = -180 / 17

Therefore, the speed of the motorboat in still water is approximately -10.59 km/h.

Answer

The speed of the motorboat in still water is approximately -10.59 km/h.