Question

Автобус виїхав із пункту А до пункта В. За першу годину він проїхав 0.25 усього шляху, за другу- 0.4 решти, за третю- 0.6 нової решти, а за четверту останні- 54 км. Знайдіть відстань між пунктами А і В

Answer 1

Весь путь =Х,
 за первый час автобус проехал 0,25Х,
за второй - 0,4 от остатка (от Х-0,25Х),
 за третий - 0,6 от нового остатка (от 0,75Х-0,4*0,75Х),
за четвертый час - 54 км.
 Всего проехал Х км.

Решаем: Х=0,25Х+0,4*0,75Х+0,6*0,45Х+54
Переносим: Х-0,25Х-0,3Х-0,27Х=54
0,18Х=54
Х=300 км.

Проверка:
За первый час проехал 0,25*300=75 км,
 за второй - 0,4 от остатка (от 300-75)= 90 км,
за третий - 0,6 от нового остатка (от 300-75-90)= 81 км,
 за четвертый час - 54 км.
Всего проехал 75+90+81+54=300 км.   Верно!

Answer 2

To find the distance between points A and B, we can add up the distances traveled during each hour of the bus journey.

Let's denote the total distance between points A and B as D.

According to the information given: - In the first hour, the bus traveled 0.25 of the total distance. - In the second hour, the bus traveled 0.4 of the remaining distance. - In the third hour, the bus traveled 0.6 of the remaining distance. - In the fourth hour, the bus traveled the remaining distance minus 54 km.

We can set up the following equation to represent the distances traveled:

0.25D + 0.4(0.75D) + 0.6(0.6D) + (D - 54) = D

Now, let's solve this equation to find the value of D, which represents the total distance between points A and B.

0.25D + 0.3D + 0.36D + D - 54 = D

Combining like terms:

1.91D - 54 = D

Subtracting D from both sides:

0.91D - 54 = 0

Adding 54 to both sides:

0.91D = 54

Dividing both sides by 0.91:

D = 54 / 0.91

Calculating the value of D:

D ≈ 59.34 km

Therefore, the distance between points A and B is approximately 59.34 km.

Please note that the calculations are based on the information provided in the question.