Question

помогите решить. Расстояние между пристанями А и В равно 80 км. Из А в В по течению реки отправился плот, а через 2 часа вслед за ним отправилась яхта, которая, прибыв в пункт В, тотчас повернула обратно и возвратилась в А. К этому времени плот прошел 22 км. Найдите скорость яхты в неподвижной воде, если скорость течения реки равна 2 км/ч. Ответ дайте в км/ч.

Answer 1

х - скорость яхты
96/(х-4)+96/(х+4) время в пути яхты
плот прошел 44 км затратив времени на 1 час больше, скорость плота 4 км/ч, 44:4=11, 11-1=10 была в пути яхта
96/(х-4)+96/(х+4)=10
96(х+4)+96(х-4)=10(х+4)(х-4)
96х+96*4+96х-96*4=10х^2-160
10x^2-192х-160=0, 5x^2-96x-80=0
х=20, второй корень отрицательный не подходит

Answer 2

Problem Analysis

We are given that the distance between two piers, A and B, is 80 km. A raft sets off from A towards B, and after 2 hours, a yacht sets off from A towards B as well. The yacht reaches point B, immediately turns back, and returns to point A. By the time the yacht reaches point B, the raft has traveled 22 km. We need to find the speed of the yacht in still water, given that the speed of the river current is 2 km/h.

Solution

Let's assume the speed of the yacht in still water is v km/h. Since the yacht is traveling against the current on its return journey, its effective speed will be reduced by the speed of the current. Therefore, the effective speed of the yacht on its return journey is v - 2 km/h.

We can calculate the time taken by the yacht to reach point B using the formula: time = distance / speed. The distance from A to B is 80 km, and the time taken by the yacht to reach B is 2 hours. Therefore, we have the equation:

80 / v = 2 (Equation 1)

We can also calculate the time taken by the yacht to return from B to A using the formula: time = distance / speed. The distance from B to A is 80 km, and the time taken by the yacht to return is the same as the time taken to reach B, which is 2 hours. Therefore, we have the equation:

80 / (v - 2) = 2 (Equation 2)

We can solve this system of equations to find the value of v, which represents the speed of the yacht in still water.

Calculation

Let's solve the system of equations (Equation 1 and Equation 2) to find the value of v.

From Equation 1, we have:

80 / v = 2

Simplifying, we get:

80 = 2v

Dividing both sides by 2, we get:

v = 40

Now, let's substitute the value of v into Equation 2:

80 / (40 - 2) = 2

Simplifying, we get:

80 / 38 = 2

Dividing both sides by 2, we get:

40 / 19 = 1

Therefore, the speed of the yacht in still water is 40 km/h.

Answer

The speed of the yacht in still water is 40 km/h.