Question

Моторная лодка за 0,4 часа по течению реки прошла на 2,5 км больше чем за 0,25 час против течения реки .Найдите собственную скорость лодки если скорость течения 2 километра в час

Answer 1

Пусть х-собственная скорость лодки. Тогда
х+2-скорость лодки по течению реки.
х-2-скорость лодки против течения реки.
(х+2)*0,4-столько км лодка прошла по течению реки.
(х-2)*0,25-столько км лодка прошла против течения реки

Известно, что по течению лодка проплыла на 2,5 км больше,чем против реки. отсюда уравнение:
0,4(х+2)-0,25(х-2)=2,5
0,4х+0,8-0,25х+0,5=2,5
0,15х+1,3=2,5
0,15х=2,5-1,3
0,15х=1,2
х=1,2/0,15
х=8
ответ:8 км/ч-собственная скорость лодки.

Answer 2

Запишем уравнение

0,4(x+2)=2.5+0.25(x-2)

0.4x+0.8=2.5+0.25x-0.5

0.4x-0.25x=2.5-0.5-0.8

0.15x=1.2

x=1.2/0.15

x=8 км/ч

Answer 3

Problem Analysis

We are given the following information: - A motorboat traveled 2.5 km farther in 0.4 hours with the current than against the current in 0.25 hours. - The speed of the current is 2 km/h.

We need to find the speed of the motorboat.

Solution

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

When the motorboat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. Therefore, the distance traveled in 0.4 hours is (x + 2) * 0.4 km.

When the motorboat is traveling against the current, its effective speed is the difference between its own speed and the speed of the current. Therefore, the distance traveled in 0.25 hours is (x - 2) * 0.25 km.

According to the given information, the distance traveled with the current is 2.5 km more than the distance traveled against the current. So we can set up the following equation:

(x + 2) * 0.4 = (x - 2) * 0.25 + 2.5

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

Calculation

Let's solve the equation step by step:

(x + 2) * 0.4 = (x - 2) * 0.25 + 2.5

Expanding the equation:

0.4x + 0.8 = 0.25x - 0.5 + 2.5

Combining like terms:

0.4x - 0.25x = 2.5 - 0.8 + 0.5

Simplifying:

0.15x = 2.2

Dividing both sides by 0.15:

x = 2.2 / 0.15

Calculating:

x = 14.67

Therefore, the speed of the motorboat is approximately 14.67 km/h.

Answer

The speed of the motorboat is approximately 14.67 km/h.