Question

Пароплав проплив 18 км за течією річки і 16 км проти течії. на шляху за течією річки він затратив часу 15 хв менше ніж на шлях проти течії. Знайдіть швидкіть течії річки, якщо швидкіть пароплава у стоячій воді дорівнює 20 км/год

Answer 1

15 мин = 1/4 часа
18 / ( 20 + X ) + ( 1/4 ) = 16 / ( 20 - X )
Общий знаменатель 4( 20 + Х )( 20 - Х )
Х >= 0 ; Х не равен 20
18•4•( 20 - Х ) + 400 - х^2 = 16•4•( 20 + Х )
1440 - 72х + 400 - х^2 = 1280 - 64х
1840 - 72х - х^2 - 1280 + 64х = 0
- х^2 - 8х + 560 = 0
D = 64 + 2240 = 2304 ; VD = 48
X1 = ( 8 + 48 ) : ( - 2 ) = - 28 ( < 0 )
X2 = ( 8 - 48 ) : ( - 2 ) = 20 ( км/час )
Ответ 20 км/час

Answer 2

Problem Analysis

We are given that a steamboat traveled 18 km downstream and 16 km upstream in a river. The time taken to travel downstream was 15 minutes less than the time taken to travel upstream. We need to find the speed of the river's current.

Solution

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

To find the speed of the steamboat in still water, we can use the formula:

Speed of steamboat in still water = Speed downstream - Speed of current (Equation 1)

We are given that the speed of the steamboat in still water is 20 km/h. Therefore, we can rewrite Equation 1 as:

20 = Speed downstream - x (Equation 2)

Similarly, the speed of the steamboat when traveling upstream can be expressed as:

20 = Speed upstream + x (Equation 3)

We are also given that the time taken to travel downstream is 15 minutes less than the time taken to travel upstream. Since time = distance / speed, we can write the following equation:

18 / (20 - x) = 16 / (20 + x) - 15/60 (Equation 4)

Now, let's solve Equation 4 to find the value of x.

Calculation

To solve Equation 4, we can cross-multiply and simplify:

18(20 + x) = 16(20 - x) - 15(20 + x)

Simplifying further:

360 + 18x = 320 - 16x - 300 - 15x

Combining like terms:

18x + 16x + 15x = 320 - 300 - 360

Simplifying:

49x = -340

Dividing both sides by 49:

x = -340 / 49

Therefore, the speed of the river's current is approximately -6.94 km/h.

Answer

The speed of the river's current is approximately -6.94 km/h.