Question

Моторная лодка прошла против течения реки 77км и вернулась в пункт отправления, затратив на обратный путь на 4 часа меньше. Найдите скорость лодки в неподвижной воде, если скорость течения равна 2км/ч. Ответ дайте в км/ч. " Только можно всё подробно расписывать"

Answer 1

Пусть скорость лодки  равна х  км/час, то по течению скорость равна х+2 км/час, соответственно против х-2 км/час , по условию  время туда она потратила больше чем на обратно то есть t2-t1=4  часа  ,выразим теперь времена через известное соотношение t=S/v
$\frac{77}{x-2}-\frac{77}{x+2}=4\\ 77(x+2)-77(x-2)=4(x-2)(x+2)\\ 4*77=4(x^2-4)\\ 308=4x^2-16\\ x=9$

ответ 9 км/час

Answer 2

Problem Analysis

We are given that a motorboat traveled 77 km against the current of a river and then returned to the starting point, spending 4 hours less on the return trip. We need to find the speed of the boat in still water, given that the speed of the current is 2 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h. The speed of the current is given as 2 km/h.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the boat's speed against the current is (x - 2) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the boat's speed with the current is (x + 2) km/h.

We are given that the boat traveled 77 km against the current and then returned to the starting point. The time taken for the return trip is 4 hours less than the time taken for the trip against the current.

Let's calculate the time taken for the trip against the current and the time taken for the return trip.

The time taken for the trip against the current can be calculated using the formula:

time = distance / speed

For the trip against the current, the distance is 77 km and the speed is (x - 2) km/h. So, the time taken for the trip against the current is:

time against current = 77 / (x - 2)

The time taken for the return trip is 4 hours less than the time taken for the trip against the current. So, the time taken for the return trip is:

time return = time against current - 4

Now, we can set up an equation using the time taken for the trip against the current and the time taken for the return trip:

time against current = time return

Substituting the values, we get:

77 / (x - 2) = (77 / (x - 2)) - 4

Simplifying the equation, we get:

77 / (x - 2) = 77 / (x - 2) - 4

Multiplying both sides of the equation by (x - 2), we get:

77 = 77 - 4(x - 2)

Simplifying further, we get:

77 = 77 - 4x + 8

Combining like terms, we get:

4x = 8

Dividing both sides of the equation by 4, we get:

x = 2

Therefore, the speed of the boat in still water is 2 km/h.

Answer

The speed of the boat in still water is 2 km/h.