Question

Теплоход на подводных крыльях шел вниз по реке со скоростью v = 80 км/ч, а вверх—со скоростью v' = 76 км/ч. Определите скорость теплохода v1 в стоячей воде и скорость v2 течения реки.

Answer 1

x-скорость  течения 

80=v+x  по течению скорость

76=v-x  скорость  против 

выведем v       v=76+x  поставим в первое уравн-е   76+x+x=80

                                                                               2x=4

                                                                                x=2км/ч скор течения

тогда    80-2=78 км/ч  теплохода в стоячей воде

 

Answer 2

Calculation of the Speed of the Boat in Still Water and the Speed of the River Current

To determine the speed of the boat in still water (v1) and the speed of the river current (v2), we can use the concept of relative velocity.

Let's assume that the speed of the boat in still water is v1 and the speed of the river current is v2.

When the boat is moving downstream (in the direction of the river current), the effective speed of the boat is the sum of its speed in still water and the speed of the river current. Therefore, the effective speed of the boat downstream is v + v2.

When the boat is moving upstream (against the direction of the river current), the effective speed of the boat is the difference between its speed in still water and the speed of the river current. Therefore, the effective speed of the boat upstream is v' - v2.

According to the given information, the boat's speed downstream (v + v2) is 80 km/h, and the boat's speed upstream (v' - v2) is 76 km/h.

Using these equations, we can set up a system of equations to solve for v1 and v2:

1. v + v2 = 80 2. v' - v2 = 76

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

Let's solve it using the method of substitution:

From equation 1, we can express v in terms of v2: v = 80 - v2

Substituting this value of v into equation 2, we get: (80 - v2)' - v2 = 76

Simplifying the equation: 80 - v2 - v2 = 76 80 - 2v2 = 76 -2v2 = 76 - 80 -2v2 = -4 v2 = -4 / -2 v2 = 2 km/h

Now that we have the value of v2, we can substitute it back into equation 1 to find v1: v + 2 = 80 v = 80 - 2 v = 78 km/h

Therefore, the speed of the boat in still water (v1) is 78 km/h and the speed of the river current (v2) is 2 km/h.

Please note that the negative sign in the value of v2 indicates that the river current is flowing in the opposite direction of the boat's motion.