Question

РАССТОЯНИЕ В 48 КМ ПО ОЗЕРУ ТЕПЛОХОД ПРОХОДИТ НА 1 Ч БЫСТРЕЕ КАТЕРА . НАЙТИ ИХ СКОРОСТЬ ЕСЛИ СКОРОСТЬ ТЕПЛОХОДА НА 4 КМ / Ч БОЛЬШЕ СКОРОСТИ КАТЕРА.

Answer 1

х (км/ч)  -  скорость катера

(х + 4) км/ч  -  скорость теплохода

$\tt\displaystyle\frac{48}{x}-\frac{48}{x+4}=1$         x≠0,  x≠-4

$\tt\displaystyle\frac{48}{x}-\frac{48}{x+4}-1=0$

$48(x+4)-48x-x(x+4)=0$

$48x+192-48x-x^{2}-4x=0$

$-x^{2}-4x+192=0$            |  × (- 1)

$x^{2}+4x-192=0$

$D=4^{2}-4*1*(- 192)=784$

$x_{1}=\tt\displaystyle\frac{-4+\sqrt{784} }{2*1}=12$ км/ч - скорость катера

$x_{2}=\tt\displaystyle\frac{-4-\sqrt{784} }{2*1}=- 16$ - не подходит под условие

$12+4=16$ км/ч - скорость теплохода.

Ответ: 12 км/ч  и  16 км/ч.

Answer 2

Calculating Speed of the Vessel and the Boat

To find the speed of the vessel and the boat, we can use the formula: Speed = Distance / Time

Given: - Distance = 48 km - Speed of the vessel = 4 km/h more than the speed of the boat - Time taken by the vessel = 1 hour less than the time taken by the boat

Let's denote the speed of the boat as B km/h and the speed of the vessel as V km/h.

Using the given information, we can form the following equations: 1. 48 = B * (T + 1), where T is the time taken by the boat 2. 48 = V * T

We can solve these equations to find the speeds of the vessel and the boat.

Solving for the Speed of the Boat and the Vessel

From the given information, we have: - 48 = B * (T + 1)- 48 = V * T- V = B + 4 (as the speed of the vessel is 4 km/h more than the speed of the boat) Substituting the value of V from the third equation into the second equation: - 48 = (B + 4) * T Now, we can solve for the values of B and T.

Calculating the Speed of the Boat and the Vessel

Using the given information and the derived equations, we can calculate the speed of the boat and the vessel.