Question

Катер отправился от пристани А до пристани В, расстояние между которыми 225 км. Через 1,5 часа после отправления он был задержан на 1/2 ч и, чтобы прийти вовремя, увеличил скорость на 10 км/ч. Найдите первоначальную скорость теплохода. схема

Answer 1

Х км/ч - начальная скорость
t=S/V
225/х=(225-1,5х)/(х+10)+0,5+1,5
225/х=(225-1,5х)/(х+10)+2
225х+2250=225х-1,5х²+2х²+20х
0,5х²+20х-2250=0
D=400+2250*0,5*4=4900
х=(-20+70)=50(км/ч)

Answer 2

Х-первоначальная скорость катера 225/х-первоначальное время 1,5хкм- путь за1,5часа (225-1,5х)км-осталось пройти катеру (х+10)км/ч-новая скорость (225-1,5х)/(х+10)-время затраченное на оставшийся путь составим уравнение (225-1,5х)/(х+10)+1,5+0,5=225/х после пробразований получим уравнение 0,5х^2+20х-2250=0. сократим на 0,5 получим уравнение х^2+40х-4500=0решая квадратное уравнение получим х=-90не подходит х=50 ответ. х=50км/ч

Answer 3

Problem Analysis

We are given that a boat traveled from port A to port B, a distance of 225 km. After 1.5 hours of departure, the boat was delayed for 0.5 hours and increased its speed by 10 km/h to arrive on time. We need to find the initial speed of the boat.

Solution

Let's assume the initial speed of the boat is x km/h.

The time taken to travel from port A to port B at the initial speed is given by: time = distance / speed = 225 / x.

After 1.5 hours, the boat was delayed for 0.5 hours, so the remaining time to reach port B is: remaining time = total time - delay time = (225 / x) - 1.5.

To arrive on time, the boat increased its speed by 10 km/h, so the new speed is x + 10 km/h.

The remaining distance to be covered at the increased speed is: remaining distance = remaining time * (x + 10) = [(225 / x) - 1.5] * (x + 10).

Since the boat arrived at port B, the remaining distance must be 0: [(225 / x) - 1.5] * (x + 10) = 0.

Let's solve this equation to find the initial speed of the boat.

Calculation

Simplifying the equation: [(225 / x) - 1.5] * (x + 10) = 0.

Expanding the equation: 225 + 10x - 1.5x - 15 = 0.

Combining like terms: 8.5x + 210 = 0.

Solving for x: 8.5x = -210.

x = -210 / 8.5.

Calculating the value of x: x ≈ -24.71.

Since speed cannot be negative, we can ignore the negative value.

Answer

The initial speed of the boat is approximately 24.71 km/h.