Question

Яхта проходит за 2 часа по течению реки на 13 км меньше, чем за 4 часа против течения. Найдите собственную скорость яхты, если скорость течения реки 3,5км/ч.

Answer 1

S/(V+3.5)=3        S=3V+10.5
S/(V-3.5)=4         S=4V-14

3V+10.5=4V-14
4V-3V=10.5+14
V=24.5 км.ч  
 

Answer 2

Calculating the Yacht's Speed

To find the yacht's speed, we can use the formula:

Speed = Distance / Time

Let's denote: - Yacht's speed as S - River's current speed as C - Distance covered by the yacht as D

Given: - The yacht takes 2 hours to cover a certain distance with the river's current. - The yacht takes 4 hours to cover the same distance against the river's current.

We can set up the following equations based on the given information:

1. With the current: - Yacht's speed + River's current speed = Speed of the yacht with the current - S + C = D / 2 2. Against the current: - Yacht's speed - River's current speed = Speed of the yacht against the current - S - C = D / 4 We also know that the distance covered by the yacht is the same in both cases.

Solving the Equations

We can solve the above equations to find the values of S and D.

Adding equations and:

(S + C) + (S - C) = D / 2 + D / 4

2S = (3D / 4)

Multiplying both sides by 2:

4S = 3D

Finding the Yacht's Speed

Now, we can solve for the yacht's speed S using the given river's current speed of 3.5 km/h.

Substituting the river's current speed C = 3.5 km/h into equation:

S + 3.5 = D / 2

Substituting the relationship 4S = 3D into the equation:

4S = 3D

We can solve for S using the above equations to find the yacht's speed.

Answer 3

Я могу помочь вам с решением задачи на движение по воде. Пусть $v$ - собственная скорость яхты, а $u$ - скорость течения реки. Тогда по условию задачи можно составить следующую систему уравнений:

$$ \begin{cases} (v+u) \cdot 2 = (v-u) \cdot 4 + 13 \\ u = 3.5 \end{cases} $$

Решая эту систему, находим, что $v = 12.75$. Ответ: собственная скорость яхты равна $12.75$ км/ч. Вы можете проверить свое решение с помощью онлайн-калькулятора или посмотреть подробное объяснение на сайте Школково. Надеюсь, я был полезен. Спасибо за обращение.