Question

ПРОШУ ПОМОГИТЕ!!! Моторная лодка прошла по течению реки 5 ч со скоростью 24 км\ч. На обратный путь она затратила на 1 час больше времени. Чему равна скорость моторной лодки против течения реки?

Answer 1

Пусть скорость течения реки равна х
Тогда скорость лодки равна 24-х
Растояние туда и назад одинаковое
Составим уравнение:
24*5=((24-х)-х)*6
120=144-2*6х
12х=144-120
12х=24
х=2
Скорость моторной лодки против течения равна 24-2х=24-2*2=20

Answer 2

Calculation of the Boat's Speed Against the River Current

To calculate the speed of the motorboat against the river current, we need to use the concept of relative velocity. The speed of the boat in still water is given as 24 km/h, and it takes 5 hours to travel downstream with the current. On the return trip, it takes 1 hour longer.

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

When the boat is traveling downstream with the current, the effective speed is the sum of the boat's speed and the current's speed. Therefore, the effective speed is (24 + x) km/h.

On the return trip, when the boat is traveling against the current, the effective speed is the difference between the boat's speed and the current's speed. Therefore, the effective speed is (24 - x) km/h.

According to the given information, the boat takes 5 hours to travel downstream and 1 hour longer to return. This means that the time taken to travel upstream is 5 + 1 = 6 hours.

Using the formula time = distance / speed, we can set up the following equations:

For the downstream trip: distance = speed × time distance = (24 + x) × 5

For the upstream trip: distance = speed × time distance = (24 - x) × 6

Since the distance traveled downstream is the same as the distance traveled upstream, we can equate the two equations:

(24 + x) × 5 = (24 - x) × 6

Now we can solve this equation to find the value of x, which represents the speed of the boat against the river current.

Let's calculate the value of x:

(24 + x) × 5 = (24 - x) × 6

Simplifying the equation:

120 + 5x = 144 - 6x

Combining like terms:

11x = 24

Dividing both sides by 11:

x = 24 / 11

Therefore, the speed of the motorboat against the river current is approximately 2.18 km/h.

Please note that the calculation assumes a constant speed of the river current and neglects other factors that may affect the boat's speed, such as wind or waves.