Question

Турист проехал на маторной лодке вверх по реке 25км, а обратно спустился на плоту.В лодке он плыл на 10 ч меньше, чем на плоту. Найдите скорость течения, если скорость лодки в стоячей воде 12 км.ч

Answer 1

x -   скорость течения 

по течению

25/x-25/(12-x)=10

  

 

 

25(12-x)-25x=10(12-x)x

300-50x=120x-10x^2

30-5x=12x-x^2

x^2-17x+30=0

D=V169=13

x=(17+13)/2=15

x=(17-13)/2=2

Ответ  2 км/час  

Answer 2

Problem Analysis

A tourist traveled upstream on a motorboat for 25 km and then returned downstream on a raft. The speed of the motorboat in still water is given as 12 km/h. The tourist traveled on the motorboat for 10 hours less than on the raft. We need to find the speed of the current.

Solution

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

When the tourist traveled upstream on the motorboat, the effective speed of the boat is reduced by the speed of the current. Therefore, the speed of the motorboat relative to the ground is 12 - x km/h.

When the tourist traveled downstream on the raft, the effective speed of the boat is increased by the speed of the current. Therefore, the speed of the raft relative to the ground is 12 + x km/h.

We are given that the tourist traveled on the motorboat for 10 hours less than on the raft. Let's assume the time taken on the raft is t hours. Therefore, the time taken on the motorboat is t + 10 hours.

We can use the formula distance = speed × time to set up two equations based on the distances traveled:

1. Distance traveled upstream on the motorboat: (12 - x) × (t + 10) = 25 km 2. Distance traveled downstream on the raft: (12 + x) × t = 25 km

We can solve these two equations to find the value of x, which represents the speed of the current.

Calculation

Let's solve the equations:

1. (12 - x) × (t + 10) = 25 2. (12 + x) × t = 25

We can rearrange equation 1 to solve for t:

(12 - x) × (t + 10) = 25

Expanding the equation:

12t + 120 - xt - 10x = 25

Combining like terms:

12t - xt - 10x = -95

Rearranging the equation:

12t - xt = 10x - 95

Dividing both sides by (12 - x):

t = (10x - 95) / (12 - x)

Substituting this value of t into equation 2:

(12 + x) × [(10x - 95) / (12 - x)] = 25

Expanding the equation:

12(10x - 95) + x(10x - 95) = 25(12 - x)

Simplifying the equation:

120x - 1140 + 10x^2 - 95x = 300 - 25x

Rearranging the equation:

10x^2 + 240x - 1140 - 95x + 25x - 300 = 0

Combining like terms:

10x^2 + 170x - 1440 = 0

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

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 10, b = 170, and c = -1440.

Substituting the values into the quadratic formula:

x = (-170 ± √(170^2 - 4 * 10 * -1440)) / (2 * 10)

Calculating the discriminant:

b^2 - 4ac = 170^2 - 4 * 10 * -1440 = 28900

Substituting the discriminant into the quadratic formula:

x = (-170 ± √28900) / 20

Calculating the square root:

√28900 = 170

Substituting the square root into the quadratic formula:

x = (-170 ± 170) / 20

Simplifying the equation:

x = 0 or x = -17

Since the speed of the current cannot be negative, we can conclude that the speed of the current is 0 km/h.

Answer

The speed of the current is 0 km/h.