Question

Моторная лодка прошла 48 км по течению реки и 70 км против течения за 4 часа.Найти скорость течения,если собственная скорость лодки равна 30 км/ч.

Answer 1

70/30-х +  48/30+х= 4
70/30-х +  48/30+х  - 4/1=0 
70(30+х)+48(30-х)-4(30-х)(30+х)=0
2100+70х+1440-48х-3600-120х+120х+4х^2=0
22x-60+4x^2=0
D=22^2-4*4*(-60)=484+960=1444
√D= √1444=38
x1= -22-38/2*4=-26.75 
x2=-22+38/2*4=2 
Ответ: 2 км/ч

Answer 2

Problem Analysis

We are given the following information: - The motorboat traveled 48 km downstream (with the current) in an unknown amount of time. - The motorboat traveled 70 km upstream (against the current) in 4 hours. - The speed of the motorboat is 30 km/h.

We need to find the speed of the current.

Downstream Speed Calculation

To find the speed of the current, we can start by calculating the speed of the motorboat when traveling downstream. We can use the formula:

Downstream speed = Boat speed + Current speed

Let's denote the downstream speed as D and the current speed as C. Given that the boat speed is 30 km/h, we have:

D = 30 + C

We also know that the motorboat traveled 48 km downstream, but we don't know the time it took. We can use the formula:

Distance = Speed × Time

Substituting the values, we have:

48 = D × T

Solving these two equations simultaneously will allow us to find the downstream speed and the time taken.

Upstream Speed Calculation

Next, let's calculate the speed of the motorboat when traveling upstream. We can use the same formula as before:

Upstream speed = Boat speed - Current speed

Let's denote the upstream speed as U. Given that the boat speed is 30 km/h, we have:

U = 30 - C

We also know that the motorboat traveled 70 km upstream in 4 hours. We can use the formula:

70 = U × 4

Solving this equation will allow us to find the upstream speed.

Solving the Equations

Now, let's solve the equations to find the downstream speed, upstream speed, and the speed of the current.

From the equation D = 30 + C, we can substitute the value of D from the equation 48 = D × T:

48 = (30 + C) × T From the equation U = 30 - C, we can substitute the value of U from the equation 70 = U × 4:

70 = (30 - C) × 4 Simplifying the equations:

48 = 30T + CT 70 = 120 - 4C Rearranging the second equation:

4C = 120 - 70 4C = 50 C = 50/4 C = 12.5 km/h

Answer

The speed of the current is 12.5 km/h.