Question

Моторная лодка проходит по реке от пункта А до пункта В расстояние за 4 часа, а обратно — за 5 часов. Определите скорость течения реки, если расстояние между пунктами 80 км.

Answer 1

Дано    t1=4 ч       t2=5 ч     S=80 км    Vр- ?

V1=Vл+Vр=S/t1
V2=Vл-Vр=S/t2

V1-V2=2*Vр= S/t1-S/t2

Vр= (S/t1-S/t2)/2=(20-16)/2=2 км/ч

Ответ Vр=2 км/ч

Answer 2

По течению лодка имеет скорость vл+vт =80/4, vл+vт =20 (1). 
Против течения лодка имеет скорость vл-vт =80/5, vл-vт =16 (2).
Из (1) вычтем (2): 2vт=4,   vт=2 км/ч.
Ответ: скорость течения 2 км/ч.

Answer 3

Calculation of River Current Speed

To determine the speed of the river current, we can use the formula:

Speed = Distance / Time

Given that the distance between points A and B is 80 km, and the boat takes 4 hours to travel from point A to point B and 5 hours to travel back from point B to point A, we can calculate the speed of the boat relative to the river current.

Let's assume the speed of the boat in still water is x km/h, and the speed of the river current is y km/h.

When the boat is traveling from point A to point B, it is moving against the current. Therefore, the effective speed of the boat is (x - y) km/h. Using the formula, we can calculate the effective speed:

80 km = (x - y) km/h * 4 hours

When the boat is traveling from point B to point A, it is moving with the current. Therefore, the effective speed of the boat is (x + y) km/h. Using the formula, we can calculate the effective speed:

80 km = (x + y) km/h * 5 hours

Now we have a system of two equations with two unknowns. We can solve this system of equations to find the values of x and y.

Let's solve the system of equations:

Equation 1: 80 = (x - y) * 4

Equation 2: 80 = (x + y) * 5

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From Equation 1, we can express x in terms of y:

x = 80/4 + y

Substituting this value of x into Equation 2:

80 = (80/4 + y + y) * 5

Simplifying the equation:

80 = (20 + 2y) * 5

80 = 100 + 10y

10y = -20

y = -2

Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:

80 = (x - (-2)) * 4

80 = (x + 2) * 4

80 = 4x + 8

4x = 72

x = 18

Therefore, the speed of the river current is 2 km/h and the speed of the boat in still water is 18 km/h.

Please note that these calculations are based on the given information and assumptions.