Question

От при­ста­ни А к при­ста­ни В от­пра­вил­ся с по­сто­ян­ной ско­ро­стью пер­вый теп­ло­ход, а через 8 часов после этого сле­дом за ним со ско­ро­стью, на 8 км/ч боль­шей, от­пра­вил­ся вто­рой. Рас­сто­я­ние между при­ста­ня­ми равно 153 км. Най­ди­те ско­рость вто­ро­го теп­ло­хо­да, если в пункт В он при­был од­но­вре­мен­но с пер­вым. Ответ дайте в км/ч.

Answer 1

Х- скорость первого теплохода , согласно условия задачи Имеем :
х+ 8 - скорость второго теплохода
153/х  -8 = 153/ (х+8) , умножим правую и левую часть уравнения на  х(х + 8)
153(х + 8) - 8*х * (х + 8) =  153*х         153х +1224 -8х^2 -64х = 153х
8х^2+64х -1224 =0        х^2 + 8х - 153 = 0 . Найдем дискриминант уравнения  =
8*8 - 4*1*(-153) = 64 + 612 = 676  . Найдем корень квадратный из дискриминанта . Он равен = 26 . Найдем корни уравнения  : 1 -ый = (-8 +26) /2*1 =18/2 = 9
2 -ой = (-8 -26)/2*1 = -34/2 = -17  . Второй корень не подходит так как он меньше нуля , а скорость меньше нуля быть не может .Скорость первого теплохода равна =9км/час , а второго 9 +8 = 17км/ч
Ответ : Скорость второго теплохода равна = 17 км/ч

Answer 2

Problem Analysis

We are given that the first steamboat travels from port A to port B at a constant speed. After 8 hours, the second steamboat departs from port A to port B at a speed that is 8 km/h faster than the first steamboat. The distance between the ports is 153 km. We need to find the speed of the second steamboat.

Solution

Let's assume the speed of the first steamboat is x km/h. Therefore, the speed of the second steamboat is x + 8 km/h.

We can use the formula distance = speed × time to calculate the time taken by each steamboat to travel from port A to port B.

For the first steamboat: - Speed = x km/h - Time = 8 hours - Distance = x × 8 km

For the second steamboat: - Speed = x + 8 km/h - Time = ? (unknown) - Distance = (x + 8) × ? km

Since both steamboats arrive at port B at the same time, the time taken by the first steamboat is equal to the time taken by the second steamboat.

Using the formula distance = speed × time, we can set up the following equation:

x × 8 = (x + 8) × ?

Simplifying the equation, we get:

8x = ?(x + 8)

To find the value of ?, we can divide both sides of the equation by (x + 8):

8x / (x + 8) = ?

Now, we can substitute the value of the distance between the ports, which is 153 km, into the equation:

8x / (x + 8) = 153

To solve this equation, we can cross-multiply:

8x = 153(x + 8)

Expanding the equation:

8x = 153x + 1224

Simplifying:

145x = 1224

Dividing both sides by 145:

x = 8.44

Therefore, the speed of the first steamboat is approximately 8.44 km/h.

To find the speed of the second steamboat, we can substitute the value of x into the expression x + 8:

x + 8 = 8.44 + 8 = 16.44

Therefore, the speed of the second steamboat is approximately 16.44 km/h.

Answer

The speed of the second steamboat is approximately 16.44 km/h.